Given,

If A and B are square matrices of the same size, then \(AB = BA\).

Step 2

Given statement is false.

For example,

Let \(A=\begin{bmatrix}1 & 0 \\2 & 3 \end{bmatrix} \text{ and } B=\begin{bmatrix}2 & 4 \\1 & 3 \end{bmatrix}\)

Then,

\(AB=\begin{bmatrix}1 & 0 \\2 & 3 \end{bmatrix}\begin{bmatrix}2 & 4 \\1 & 3 \end{bmatrix}\)

\(=\begin{bmatrix}2 & 4 \\7 & 17 \end{bmatrix}\)

and

\(BA=\begin{bmatrix}2 & 4 \\1 & 3 \end{bmatrix}\begin{bmatrix}1 & 0 \\2 & 3 \end{bmatrix}\)

\(=\begin{bmatrix}10 & 12 \\7 & 9 \end{bmatrix}\)

Clearly \(AB \neq BA\)