Question

lf $A=\left\{\begin{array}{cc}2& 2\\ -3& 2\end{array}\right\},B=\left\{\begin{array}{cc}0& -1\\ 1& 0\end{array}\right\}$, 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 $\left\{\begin{array}{cc}2& -2\\ 2& 3\end{array}\right\}$

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