Question

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

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

Answer 1

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

We know, using properties of inverse matrix, $(B^{-1}{A}^{-1}{)}^{-1}=(A^{-1}{)}^{-1}(B^{-1}{)}^{-1}=AB$
$\therefore (B^{-1}{A}^{-1}{)}^{-1}=\left[\begin{array}{cc}2& 2\\ -3& 2\end{array}\right]\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$
$\Rightarrow (B^{-1}{A}^{-1}{)}^{-1}=\left[\begin{array}{cc}2& -2\\ 2& 3\end{array}\right]$