Answer
Yes they are inverses of each other.
Work Step by Step
Multiply the two matrices together. If their product equals to the identity matrix, then they are inverses of each other.
$\begin{array}{l}
\left[ {\begin{array}{*{20}{c}}
2&3&{ - 1}\\
1&2&1\\
{ - 1}&{ - 1}&3
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
7&{ - 8}&5\\
{ - 4}&5&{ - 3}\\
1&{ - 1}&1
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
{2(7) + 3( - 4) + ( - 1)(1)}&{2( - 8) + 3(5) + ( - 1)( - 1)}&{2(5) + 3( - 3) + ( - 1)(1)}\\
{1(7) + 2( - 4) + 1(1)}&{1( - 8) + 2(5) + 1( - 1)}&{1(5) + 2( - 3) + 1(1)}\\
{ - 1(7) + ( - 1)( - 4) + 3(1)}&{ - 1( - 8) + ( - 1)5 + 3( - 1)}&{ - 1(5) + ( - 1)( - 3) + 3(1)}
\end{array}} \right]\\
= \left[ {\begin{array}{*{20}{c}}
1&0&0\\
0&1&0\\
0&0&1
\end{array}} \right]
\end{array}$
