Answer
See answer below
Work Step by Step
Matrices are inverses of one another if
$AA^{-1}=A^{-1}A=I_n$
hence
$AA^{-1}=\begin{bmatrix}
3 & 5&1\\
1 &2 &1\\
2 & 6 & 7
\end{bmatrix}.\begin{bmatrix}
8 & -29&3\\
-5 &19 &-2\\
2 & -8 & 1
\end{bmatrix}=\begin{bmatrix}
1 & 0&0\\
0 &1 &0\\
0 & 0 & 1
\end{bmatrix}$
$A^{-1}A=\begin{bmatrix}
8 & -29&3\\
-5 &19 &-2\\
2 & -8 & 1
\end{bmatrix}.\begin{bmatrix}
3 & 5&1\\
1 &2 &1\\
2 & 6 & 7
\end{bmatrix}=\begin{bmatrix}
1 & 0&0\\
0 &1 &0\\
0 & 0 & 1
\end{bmatrix}$
It shows that the given matrices are inverses of one another.
