logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Matrices
0 votes

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

$\begin{array}{1 1}(a)\;a=0,b=c&(b)\;b=0,c=d\\(c)\;c=0,d=a&(d)\;d=0,a=b\end{array}$

Can you answer this question?
 
 

1 Answer

0 votes
Since matrix $\begin{bmatrix}a&b\\c&d\end{bmatrix}$ is commutative with the matrix $\begin{bmatrix}1&1\\0&1\end{bmatrix}$
$\Rightarrow \begin{bmatrix}a&b\\c&d\end{bmatrix}\begin{bmatrix}1&1\\0&1\end{bmatrix}=\begin{bmatrix}1&1\\0&1\end{bmatrix}\begin{bmatrix}a&b\\c&d\end{bmatrix}$
$\Rightarrow \begin{bmatrix}a&a+b\\c&c+d\end{bmatrix}=\begin{bmatrix}a+c&b+d\\c&d\end{bmatrix}$
$\Rightarrow a=a+c,a+b=b+d$
$\Rightarrow c=0,a=d$
Hence (c) is the correct answer.
answered Nov 22, 2013 by sreemathi.v
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...