Answer
See explanations.
Work Step by Step
Step 1. List the matrices to be tested:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 2&-5\\ -2&6 \end{bmatrix},
\begin{array} \\B=\\ \end{array}
\begin{bmatrix} 3&5/2\\ 1&1 \end{bmatrix} $
Step 2. Perform the operation:
$\begin{array} \\AB=\\ \end{array}
\begin{bmatrix} 2&-5\\ -2&6 \end{bmatrix}
\begin{bmatrix} 3&5/2\\ 1&1 \end{bmatrix}
=\begin{bmatrix} 6-5&5-5\\ -6+6&-5+6 \end{bmatrix}
=\begin{bmatrix} 1&0\\ 0&1 \end{bmatrix} $
Step 3. Perform the operation:
$\begin{array} \\BA=\\ \end{array}
\begin{bmatrix} 3&5/2\\ 1&1 \end{bmatrix}
\begin{bmatrix} 2&-5\\ -2&6 \end{bmatrix}
=\begin{bmatrix} 6-5&-15+15\\ 2-2&-5+6 \end{bmatrix}
=\begin{bmatrix} 1&0\\ 0&1 \end{bmatrix} $
Step 4. Conclusion: we confirmed that matrices A and B are inverses to each other.
