Here $|\mathrm{A}|=\left|\begin{array}{ll}3 & 7 \\ 2 & 5\end{array}\right|=15-14=1 \neq 0$
$\therefore \quad \operatorname{Adj} A=\left[\begin{array}{cc}5 & -7 \\ -2 & 3\end{array}\right]$
Hence, $\mathrm{A}^{-1}=\frac{1}{|\mathrm{~A}|}$ Adj. $\mathrm{A}=\left[\begin{array}{cc}5 & -7 \\ -2 & 3\end{array}\right]$
$[\because|\mathrm{A}|=1]$
Also, $|\mathrm{B}|=\left|\begin{array}{ll}6 & 8 \\ 7 & 9\end{array}\right|=54-56=-2 \neq 0$
$\therefore \quad \operatorname{Adj} B=\left[\begin{array}{cc}9 & -8 \\ -7 & 6\end{array}\right]$
Hence, $\mathrm{B}^{-1}=\frac{1}{|\mathrm{~B}|}$ Adj. $\mathrm{B}=-\frac{1}{2}\left[\begin{array}{cc}9 & -8 \\ -7 & 6\end{array}\right]$ $\mathrm{B}^{-1} \mathrm{~A}^{-1}$
$\begin{aligned}
&=-\frac{1}{2}\left[\begin{array}{cc}
9 & -8 \\
-7 & 6
\end{array}\right]\left[\begin{array}{cc}
5 & -7 \\
-2 & 3
\end{array}\right] \\
&=-\frac{1}{2}\left[\begin{array}{cc}
61 & -87 \\
-47 & 67
\end{array}\right] \\
&\text { Now, }|\mathrm{AB}|=|\mathrm{A}||\mathrm{B}|=1 \times(-2)=-2 \neq 0 \\
&\text { AdjAB }=(\mathrm{Adj} \mathrm{B})(\mathrm{Adj} A) \\
&=\left[\begin{array}{cc}
9 & -8 \\
-7 & 6
\end{array}\right]\left[\begin{array}{cc}
5 & -7 \\
-2 & 3
\end{array}\right]=\left[\begin{array}{cc}
61 & -87 \\
-47 & 67
\end{array}\right] \\
&\mathrm{AB}^{-1}=\frac{1}{-2}\left[\begin{array}{cc}
61 & -87 \\
-47 & 67
\end{array}\right]
\end{aligned}$
Hence, $(\mathrm{AB})^{-1}=\mathrm{B}^{-1} \mathrm{~A}^{-1}$.