# Determine whether each of the following statements is true or false, and explain why.If A and B are square matrices of the same size, then AB = BA

Determine whether each of the following statements is true or false, and explain why.If A and B are square matrices of the same size, then $AB=BA$

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Malena

Given,
If A and B are square matrices of the same size, then $AB=BA$.
Step 2
Given statement is false.
For example,
Let
Then,
$AB=\left[\begin{array}{cc}1& 0\\ 2& 3\end{array}\right]\left[\begin{array}{cc}2& 4\\ 1& 3\end{array}\right]$
$=\left[\begin{array}{cc}2& 4\\ 7& 17\end{array}\right]$
and
$BA=\left[\begin{array}{cc}2& 4\\ 1& 3\end{array}\right]\left[\begin{array}{cc}1& 0\\ 2& 3\end{array}\right]$
$=\left[\begin{array}{cc}10& 12\\ 7& 9\end{array}\right]$
Clearly $AB\ne BA$

Jeffrey Jordon

Answer is given below (on video)