Answer
The given matrices are inverses of one another.
Work Step by Step
Matrices are inverses of one another if
$AA^{-1}=A^{-1}A=I_n$
hence
$AA^{-1}=\begin{bmatrix}
4 & 9\\
3 & 7
\end{bmatrix}.\begin{bmatrix}
7 & -9\\
-3 & 4
\end{bmatrix}=\begin{bmatrix}
1 &0\\
0& 1
\end{bmatrix}$
$A^{-1}A=\begin{bmatrix}
7& -9\\
-3 & 4
\end{bmatrix}.\begin{bmatrix}
4& 9\\
3& 7
\end{bmatrix}=\begin{bmatrix}
1 & 0\\
0& 1
\end{bmatrix}$
It shows that the given matrices are inverses of one another.
