Question

If $\left[\begin{array}{cc}2& 1\\ 7& 4\end{array}\right]A\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ then matrix A equals

• A. $\left[\begin{array}{cc}7& 5\\ -11& -8\end{array}\right]$
• B. $\left[\begin{array}{cc}2& 1\\ 5& 3\end{array}\right]$
• C. $\left[\begin{array}{cc}7& 1\\ 34& 5\end{array}\right]$
• D. none of these

Answer 1

The correct option is A $\left[\begin{array}{cc}7& 5\\ -11& -8\end{array}\right]$

$\left[\begin{array}{cc}2& 1\\ 7& 4\end{array}\right]A\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

$\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]=\left[\begin{array}{cc}-3& -2\\ -5& -3\end{array}\right]\times \frac{1}{(9-10)}$

${\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]}^{-1}=\left[\begin{array}{cc}3& 2\\ 5& 3\end{array}\right]$..........(1)

$\left[\begin{array}{cc}2& 1\\ 7& 4\end{array}\right]A\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]{\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]}^{-1}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]{\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]}^{-1}$

$\left[\begin{array}{cc}2& 1\\ 7& 4\end{array}\right]A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]\left[\begin{array}{cc}3& 2\\ 5& 3\end{array}\right]=\left[\begin{array}{cc}3& 2\\ 5& 3\end{array}\right]$

$\left[\begin{array}{cc}2& 1\\ 7& 4\end{array}\right]A=\left[\begin{array}{cc}3& 2\\ 5& 3\end{array}\right]$

${\left[\begin{array}{cc}2& 1\\ 7& 4\end{array}\right]}^{-1}=\frac{1}{(8-7)}\left[\begin{array}{cc}4& -1\\ -7& 2\end{array}\right]$

${\left[\begin{array}{cc}2& 1\\ 7& 4\end{array}\right]}^{-1}=\left[\begin{array}{cc}4& -1\\ -7& 2\end{array}\right]$

${\left[\begin{array}{cc}2& 1\\ 7& 4\end{array}\right]}^{-1}\left[\begin{array}{cc}2& 1\\ 7& 4\end{array}\right]A=\left[\begin{array}{cc}4& -1\\ -7& 2\end{array}\right]\left[\begin{array}{cc}3& 2\\ 5& 3\end{array}\right]$

$A=\left[\begin{array}{cc}(12-5)& (8-3)\\ (-21+10)& (-14+6)\end{array}\right]$

$A=\left[\begin{array}{cc}7& -11\\ 5& -8\end{array}\right]$