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 ${\left(B^{-1}{A}^{-1}\right)}^{-1}=$ _______.

Answer 1

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

Hence, this is the answer.