Draw the truth table for the compound statement (p q) and write A B and (A B) in simple English.

$$
Q^T = \begin{pmatrix} 2 & x-2 \\ 3 & x \end{pmatrix}
$$
$$
\boxed{Q^T = \begin{pmatrix} 2 & x-2 \\ 3 & x \end{pmatrix}}
$$

$$
\begin{pmatrix} 2 & 3 \\ x-2 & x \end{pmatrix} = \begin{pmatrix} 2 & x-2 \\ 3 & x \end{pmatrix}
$$

$$
3 = x-2
$$

$$
x = 3+2
$$
$$
x = 5
$$
(Also, $x-2 = 3$ gives $x=5$, and the diagonal elements $2=2$ and $x=x$ are always equal).
$$
\boxed{x=5}
$$

$$
P^2 = \begin{pmatrix} 4 & 3 \\ 1 & 2 \end{pmatrix} \begin{pmatrix} 4 & 3 \\ 1 & 2 \end{pmatrix}
$$

The element in row $i$, column $j$ of the product matrix is the dot product of row $i$ of the first matrix and column $j$ of the second matrix.
$$
P^2 = \begin{pmatrix} (4)(4) + (3)(1) & (4)(3) + (3)(2) \\ (1)(4) + (2)(1) & (1)(3) + (2)(2) \end{pmatrix}
$$
$$
P^2 = \begin{pmatrix} 16 + 3 & 12 + 6 \\ 4 + 2 & 3 + 4 \end{pmatrix}
$$
$$
P^2 = \begin{pmatrix} 19 & 18 \\ 6 & 7 \end{pmatrix}
$$
$$
\boxed{P^2 = \begin{pmatrix} 19 & 18 \\ 6 & 7 \end{pmatrix}}
$$