# Recent questions tagged matrices-and-determinants

### If $\alpha, \beta \neq 0$, and $f(n) = \alpha^n+\beta^n$ and $\begin{vmatrix} 3 & 1+f(1) & 1+f(2)\\ 1+f(1)& 1+f(2) &1+f(3) \\ 1+f(2)&1+f(3) & 1+f(4) \end{vmatrix}$$=K(1-\alpha)^2\;(1-\beta)^2\;(\alpha-\beta)^2, then K is equal to ### If A is an 3\times 3 non-singular matrix such that A A' = A' A and B = A^{-1} A', then B B' equals ### Given A=\begin{bmatrix} 3 & -3 & 4 \\2 & -3 & 4 \\0 & -1 & 1 \end{bmatrix} How can we express A^{-1} in terms of A? ### If A=\begin{bmatrix}2 & sec^{-1}x\\-1 & cosec^{-1} x \end{bmatrix} is a singular matrix then find the value of x ### Inverse of \begin{bmatrix}1&2&3\\2&3&4\\3&4&6\end{bmatrix} is ### If A=\begin{bmatrix}3 & 2\\1 & 1\end{bmatrix} find the values of a and b, such that A^2+aA+bI=0. ### If \;A=\small\frac{1}{\pi}$$\begin{bmatrix}sin^{-1}(\pi x) &tan^{-1}\big(\frac{\pi}{x}\big)\\ sin^{-1}\big(\frac{\pi}{x} \big)&cot^{-1}(\pi x)\end{bmatrix}\;$ and $\;B=\small\frac{1}{\pi}$$\begin{bmatrix}-cos^{-1}(\pi x) &tan^{-1}\big(\frac{x}{\pi}\big)\\ sin^{-1}\big(\frac{x}{\pi} \big)&-tan^{-1}(\pi x)\end{bmatrix}$ then $A-B$ is equal to

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