Answer
See explanations.
Work Step by Step
Step 1. List the matrices to be tested:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 2&-1&3\\ 2&-2&1\\0&1&1 \end{bmatrix},
\begin{array} \\B=\\ \end{array}
\begin{bmatrix} -3/2&2&5/2\\ -1&1&2\\1&-1&-1 \end{bmatrix}$
Step 2. Perform the operation:
$\begin{array} \\AB=\\ \end{array}
\begin{bmatrix} 2&-1&3\\ 2&-2&1\\0&1&1 \end{bmatrix}
\begin{bmatrix} -3/2&2&5/2\\ -1&1&2\\1&-1&-1 \end{bmatrix}
=\begin{bmatrix} -3+1+3&4-1-3&5-2-3\\ -3+2+1&4-2-1&5-4-1\\-1+1&1-1&2-1 \end{bmatrix}
=\begin{bmatrix} 1&0&0\\ 0&1&0\\0&0&1 \end{bmatrix}$
Step 3. Perform the operation:
$\begin{array} \\BA=\\ \end{array}
\begin{bmatrix} -3/2&2&5/2\\ -1&1&2\\1&-1&-1 \end{bmatrix}
\begin{bmatrix} 2&-1&3\\ 2&-2&1\\0&1&1 \end{bmatrix}
=\begin{bmatrix} -3+4+0&3/2-4+5/2&-9/2+2+5/2\\-2+2+0&1-2+2&-3+1+2\\2-2+0&-1+2-1&3-1-1 \end{bmatrix}
=\begin{bmatrix} 1&0&0\\ 0&1&0\\0&0&1 \end{bmatrix}$
Step 4. Conclusion: we confirmed that matrices A and B are inverses of each other.
