Answer
False.
Work Step by Step
(See Example 6 on page 619)
A=[ 1 2 3 ] , B=$\left[\begin{array}{l}
4\\
5\\
6
\end{array}\right]$
AB=[ 32 ]
BA=$\left[\begin{array}{lll}
4 & 8 & 12\\
5 & 10 & 15\\
6 & 12 & 18
\end{array}\right]$
that is, $AB\neq BA$
Or, what can happen is that AB is defined, but BA is not:
Let A be a 2$\times$3 matrix and B be a 3$\times$4 matrix.
The number of columns in A = number of rows in B, so AB exists and is a 2$\times$4 matrix.
But,
the number of columns in B $\neq$ number in rows in A, so BA does not exist.
So, not always is AB=BA,
multiplication of matrices is not commutative.
The statement is false.
