Question

If $\left[\begin{array}{cc}2& 1\\ 3& 2\end{array}\right]A\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ then the matrix A is equal to

• A. $\left[\begin{array}{cc}1& 1\\ 1& 0\end{array}\right]$
• B. $\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]$
• C. $\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]$
• D. $\left[\begin{array}{cc}0& 1\\ 1& 1\end{array}\right]$

Answer 1

The correct option is A $\left[\begin{array}{cc}1& 1\\ 1& 0\end{array}\right]$

$\left[\begin{array}{cc}2& 1\\ 3& 2\end{array}\right]A\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

Pro multiplying by inverse of 1st matrix on LHS

$A\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]=\left[\begin{array}{cc}2& -3\\ -1& 2\end{array}\right]\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}2& -3\\ -1& 2\end{array}\right]$

$A\left[\begin{array}{cc}-3& 2\\ 5-3& \end{array}\right]=\left[\begin{array}{cc}2& -3\\ -1& 2\end{array}\right]$

Post multiplying by 2nd matrix.

$A=\left[\begin{array}{cc}2& -3\\ -1& 2\end{array}\right]\left[\begin{array}{cc}-3& -5\\ -2& -3\end{array}\right]$

$=\left[\begin{array}{cc}1& 1\\ 1& 0\end{array}\right]$