Question

Prove that $A=(\begin{array}{cc}5& 2\\ 7& 3\end{array})$ and $B=(\begin{array}{cc}3& -2\\ -7& 5\end{array})$ are inverses to each other under matrix multiplication.

Answer 1

$=\left[\begin{array}{cc}15-14& -10+10\\ 21-21& -14+15\end{array}\right]$

$=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

$\Rightarrow AB=I$

We know that if the product of two matrices is an identity then the two matrices are multiplicative inverse of each other.

Hence, solved.