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Questions >> JEEMAIN and NEET >> Mathematics >> Class12 >> Matrices

If $A,B$ are two square matrices such that $AB=A$ and $BA=B$ then $A$ and $B$ are

answered Apr 25, 2014 by sreemathi.v

1 answer

If $A$ is orthogonal matrix then

answered Apr 25, 2014 by sreemathi.v

1 answer

The number of right inverse for the matrix $\begin{bmatrix}1&-1&2\\2&-1&1\end{bmatrix}$

answered Apr 25, 2014 by sreemathi.v

1 answer

If $A$ is an invertible matrix and B is a matrix then

answered Apr 24, 2014 by sreemathi.v

1 answer

$\begin{vmatrix}\log_3512&\log_43\\\log_38&\log_49\end{vmatrix}\times \begin{vmatrix}\log_23&\log_83\\\log_34&\log_34\end{vmatrix}=$

answered Apr 24, 2014 by sreemathi.v

1 answer

Let $C=\begin{bmatrix}C_{11}&C_{12}\\C_{21}&C_{22}\end{bmatrix}$ be a $2\times 2$ matrix and there exist $2\times 2$ matrices $A$ and $B$ such that $C=AB-BA$ then

answered Apr 24, 2014 by sreemathi.v

1 answer

If $a,b,c$ are all different and $\begin{vmatrix}a&a^3&a^4-1\\b&b^3&b^4-1\\c&c^3&c^4-1\end{vmatrix}=0$ then the value of $abc(ab+bc+ca)$ is

answered Apr 24, 2014 by sreemathi.v

1 answer

If $a=1+2+4+.........$ upto n terms, $b=1+3+9+.....$ upto n terms, $c=1+5+25+.....$ upto n terms then $\begin{vmatrix}a&2b&4c\\2&2&2\\2^n&3^n&5^n\end{vmatrix}=$

answered Apr 23, 2014 by sreemathi.v

1 answer

The value of $\begin{vmatrix}a&a+b&a+2b\\a+2b&a&a+b\\a+b&a+2b&a\end{vmatrix}$ is equal to

answered Apr 23, 2014 by sreemathi.v

1 answer

If $p\neq a,q\neq b,r\neq c$ and $\begin{vmatrix}p&b&c\\p+a&q+b&2c\\a&b&r\end{vmatrix}=0$ then $\large\frac{p}{p-a}+\frac{q}{q-b}+\frac{r}{r-c}$ =

answered Apr 23, 2014 by sreemathi.v

1 answer

If $A=\begin{bmatrix}0&2\\3&-4\end{bmatrix}$ and $kA=\begin{bmatrix}0&3a\\2b&24\end{bmatrix}$ then the values of $k,a,b$ are respectively

answered Apr 23, 2014 by sreemathi.v

1 answer

If $A=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}$ then $A^5=$

answered Apr 23, 2014 by sreemathi.v

1 answer

If $\begin{vmatrix}x+\alpha&\beta&\gamma\\\alpha&x+\beta&\gamma\\\alpha&\beta&x+\gamma\end{vmatrix}=0$ then $4x$ is equal to

answered Apr 23, 2014 by sreemathi.v

1 answer

If $A$ and $B$ are two matrices such that $AB=B$ and $BA=A$ then $A^2+B^2=$

answered Apr 23, 2014 by sreemathi.v

1 answer

For each real numbers $x$ such that $-1 < x < 1$ let $A(x)$ be the matrix. $(1-x)^{-\large\frac{1}{2}}\begin{bmatrix}1&-x\\-x&1\end{bmatrix}$ and $z=\large\frac{x+y}{1+xy}$ .Then

answered Apr 23, 2014 by sreemathi.v

1 answer

The roots of the equation $\begin{vmatrix}x-1&1&1\\1&x-1&1\\1&1&x-1\end{vmatrix}=0$ are

answered Apr 23, 2014 by sreemathi.v

1 answer

If a matrix A is such that $3A^3+2A^2+5A+I=0$ then its inverse is

answered Apr 23, 2014 by sreemathi.v

1 answer

If $A=\begin{bmatrix}0&1&0\\0&0&1\\1&-1&0\end{bmatrix}$ then $A^3+A$ equals

answered Apr 23, 2014 by sreemathi.v

1 answer

If $A$ and $B$ are square matrices of the same order and A is non-singular then for a positive integer n, $(A^{-1}BA)^n$ is equal to

answered Apr 23, 2014 by sreemathi.v

1 answer

If $a,b,c$ are in A.P with common difference d and $\begin{vmatrix}x+1&x+a&x+b\\x+a&x+b&x+c\\x-b+1&x-1&x-a+c\end{vmatrix}$ has absolute value 2 then d is

answered Apr 23, 2014 by sreemathi.v

1 answer

If $f(n)=\begin{vmatrix} n& 1&5\\n^2&2r+1&2r+1\\n^3&3r^2&3r+1\end{vmatrix}$ then $\sum\limits_{n=1}^ r f(n)$ is

answered Apr 22, 2014 by sreemathi.v

1 answer

If $S_r=\begin{vmatrix}2r&x&n(n+1)\\6r^2-1&y&n^2(2n+3)\\4r^32nr&z&n^3(n+1)\end{vmatrix}$ then value of $\sum\limits_{r=1}^n S_r$ is independent of

answered Apr 22, 2014 by sreemathi.v

1 answer

The repeated factor of $\begin{vmatrix}y+z&x&y\\z+x& z&x\\x+y& y&z\end{vmatrix}$ is

answered Apr 22, 2014 by sreemathi.v

1 answer

If $a,b,c$ are non zero real numbers,then $\begin{vmatrix}bc&ca&ab\\ca&ab&bc\\ab&bc&ca\end{vmatrix}$ vanishes when

answered Apr 22, 2014 by sreemathi.v

1 answer

If a point $(x,y)$ moves on a curve and satisfies the equation $\small\begin{vmatrix}a&b&ax+by\\b&c&bx+cy\\ax+by&bx+ay&0\end{vmatrix}=0$ then

answered Nov 26, 2013 by sreemathi.v

1 answer

If a square matrices $A$ and $B$ are such that $AA^{\theta}=A^{\theta}A$ , $BB^{\theta}=B^{\theta}B$ , $AB^{\theta}=B^{\theta}A$ then $AB(AB)^{\theta}$ is equal to

answered Nov 26, 2013 by sreemathi.v

1 answer

Matrix $A$ satisfies $A^2=2A-I$ where $I$ is the identity matrix. For $n \geq 2$ , $A^n$ is equal to $(n\in N)$

answered Nov 25, 2013 by sreemathi.v

1 answer

If a square matrix A is such that $AA^T=I=A^TA$ then $\mid A\mid$ is equal to

answered Nov 25, 2013 by sreemathi.v

1 answer

If $\begin{vmatrix}x-1&5x&7\\x^2-1&x-1&8\\2x&3x&0\end{vmatrix}$ = $ax^3+bx^2+cx+d$ then $c$ is equal to

answered Nov 25, 2013 by sreemathi.v

1 answer

The characteristic root of the matrix $\begin{bmatrix}1&0&0\\2&3&0\\4&5&6\end{bmatrix}$ are

answered Nov 25, 2013 by sreemathi.v

1 answer

If $x,y,z$ are all distinct and $\begin{vmatrix}x&x^2&1+x^3\\y&y^2&1+y^3\\z&z^2&1+z^3\end{vmatrix}=0$ then the value of $xyz$ is

answered Nov 25, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}6&8&5\\4&2&3\\9&7&1\end{bmatrix}$ is the sum of symmetric matrix $B$ and skew-symmetric matrix $C$ then $B$ is

answered Nov 25, 2013 by sreemathi.v

1 answer

A skew-symmetric matrix S satisfies the relation $S^2+I=0$ where $I$ is a unit matrix. Then $SS'$ is equal to

answered Nov 25, 2013 by sreemathi.v

1 answer

If $\begin{bmatrix}0&a\\b&0\end{bmatrix}^4=I$ then

answered Nov 25, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}3&3&3\\3&3&3\\3&3&3\end{bmatrix}$ then $A^4$ is equal to

answered Nov 25, 2013 by sreemathi.v

1 answer

The value of $\begin{vmatrix}x&p&q\\p&x&q\\p&q&x\end{vmatrix}$ is

answered Nov 22, 2013 by sreemathi.v

1 answer

If $A$ and $B$ are square matrices of the same order and $AB=3I$ then $A^{-1}$ is equal to

answered Nov 22, 2013 by sreemathi.v

1 answer

If $A$ and $B$ are square matrices of the same order such that $(A+B)(A-B)=A^2-B^2$ then $(ABA^{-1})^2$ is equal to

answered Nov 22, 2013 by sreemathi.v

1 answer

If the matrix $\begin{bmatrix}a&b\\c&d\end{bmatrix}$ is commutative with the matrix $\begin{bmatrix}1&1\\0&1\end{bmatrix}$ then

answered Nov 22, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1&-2\\4&5\end{bmatrix}$ and $f(1)=t^2-3t+7$ then $f(A)+\begin{bmatrix}3&6\\-12&-9\end{bmatrix}$ is equal to

answered Nov 22, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1&2&2\\2&1&2\\2&2&1\end{bmatrix}$ then $A^2-4A$ is equal to

answered Nov 22, 2013 by sreemathi.v

1 answer

If $\small\begin{vmatrix}a^2&b^2&c^2\\(a+1)^2&(b+1)^2&(c+1)^2\\(a-1)^2&(b-1)^2&(c-1)^2\end{vmatrix}$ = $k\small\begin{vmatrix}a^2&b^2&c^2\\a&b&c\\1&1&1&\end{vmatrix}$ then the value of $k$ is

answered Nov 22, 2013 by sreemathi.v

1 answer

If the matrix $A=\begin{bmatrix}y+a&b&c\\a&y+b&c\\a&b&y+c\end{bmatrix}$ has rank 3 then

answered Nov 22, 2013 by sreemathi.v

1 answer

If $\begin{bmatrix}2&1\\3&2\end{bmatrix}A\begin{bmatrix}-3&2\\5&-3\end{bmatrix}=\begin{bmatrix}1&0\\0&1\end{bmatrix}$ then the matrix A is equal to

answered Nov 22, 2013 by sreemathi.v

1 answer

If $A$ is a square matrix such that $A^2=I$ then $A^{-1}$ is equal to

answered Nov 21, 2013 by sreemathi.v

1 answer

Let $A=\begin{vmatrix}5 &5\alpha&\alpha\\0&\alpha&5\alpha\\0&0&5\end{vmatrix}$ if $\mid A^2\mid=25$ then $\alpha$ equals

answered Nov 21, 2013 by sreemathi.v

1 answer

Let $A=\begin{bmatrix}1&2\\3&4\end{bmatrix}$ and $B=\begin{bmatrix}a&0\\0&b\end{bmatrix}\;a,b\in N$ .Then

answered Nov 21, 2013 by sreemathi.v

1 answer

If $A$ and $B$ are square matrices of size $n\times n$ such that $A^2-B^2=(A-B)(A+B)$ then which of the following will be always true?

answered Nov 21, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}a&b\\b&a\end{bmatrix}$ and $A^2=\begin{bmatrix}\alpha&\beta\\\beta&\alpha\end{bmatrix}$ then

answered Nov 21, 2013 by sreemathi.v

1 answer

Let $\omega$ be a complex cube root of unity with $\omega\neq 1$ and $p=[P_{ij}]$ be a $n\times n$ matrix with $P_{ij}=\omega^{i+j}$ .Then $P^2\neq 0$ when $n$ =

answered Nov 21, 2013 by sreemathi.v

1 answer

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