Question

If $A=\left[\begin{array}{cc}2& 2\\ -3& 2\end{array}\right],B=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right],$ then $(B^{-1}{A}^{-1}{)}^{-1}=$

• A. $\left[\begin{array}{cc}2& -2\\ 2& 3\end{array}\right]$
• B. $\left[\begin{array}{cc}3& -2\\ 2& 2\end{array}\right]$
• C. $\frac{1}{10}\left[\begin{array}{cc}2& 2\\ -2& 3\end{array}\right]$
• D. $\frac{1}{10}\left[\begin{array}{cc}3& 2\\ -2& 2\end{array}\right]$

Answer 1

The correct option is A $\left[\begin{array}{cc}2& -2\\ 2& 3\end{array}\right]$

$(B^{-1}{A}^{-1}{)}^{-1}=(A^{-1}{)}^{-1}.(B^{-1}{)}^{-1}=AB$
$\therefore AB=\left[\begin{array}{cc}2& 2\\ -3& 2\end{array}\right]\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]=\left[\begin{array}{cc}2& -2\\ 2& 3\end{array}\right]$