We are given two matrices $A$ and $B$, and the task is to find matrix $C$, which is given by the formula:

$C = A^2 - (AB)^T + 3E$

Where:

• $A^2$ is the square of matrix $A$ (i.e., $A \times A$),
• $(AB)^T$ is the transpose of the product of matrices $A$ and $B$,
• $E$ is the identity matrix of the same size as $A$ and $B$.

Let's break down the problem:

Step 1: Define the matrices

Matrix $A$ and $B$ are:

$A = \begin{pmatrix} 5 & -6 \\ 0 & -1 \end{pmatrix}, \quad B = \begin{pmatrix} -1 & 1 \\ 3 & 2 \end{pmatrix}$

Step 2: Calculate $A^2$

First, we find the square of matrix $A$, i.e., $A \times A$.

$A^2 = \begin{pmatrix} 5 & -6 \\ 0 & -1 \end{pmatrix} \times \begin{pmatrix} 5 & -6 \\ 0 & -1 \end{pmatrix}$

$A^2 = \begin{pmatrix} 5 \times 5 + (-6) \times 0 & 5 \times (-6) + (-6) \times (-1) \\ 0 \times 5 + (-1) \times 0 & 0 \times (-6) + (-1) \times (-1) \end{pmatrix}$