the inverse of a two-by-two matrix
A=[tex] \left[\begin{array}{ccc}a&b\\c&d\end{array}\right] [/tex]
whose inverse is
[tex]A^{-1}=\frac{\left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right]}{ad-bc}[/tex]
Substituting values, we get
[tex]A^{-1}=\frac{\left[\begin{array}{ccc}7&9\\-8&-5\end{array}\right]}{37}[/tex]
which is not the same as matrix B. Therefore B is not the inverse of A.
We can prove similarly that A is not the inverse of B.
