Question

If $A=\left[\begin{array}{cc}2& -1\\ 3& 4\end{array}\right]$ find $|(A^{-1}{)}^{-1}|$.

Answer 1

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

$\Rightarrow \left|{\left(A^{-1}\right)}^{-1}\right|=\left|A\right|$ $\{\because {\left(A^{-1}\right)}^{-1}=A\}$

$\Rightarrow \left[\begin{array}{cc}2& -1\\ 3& 4\end{array}\right]=8-(3x-1)=8+3=11.$

Hence, the answer is $11.$