Question

If $A =\begin{bmatrix}1& -2& 3\\ -4&2&5\end{bmatrix}$ and $ B = \begin{bmatrix}2&3\\ 4&5\\ 2&1\end{bmatrix} $, then

• A. AB, BA exist and are equal
• B. AB, BA exist and are not equal
• C. AB exists and BA does not exist
• D. AB does not exist and BA exists

Answer 1

Answer: (B)

A is 2 $\times $ 3 matrix and B is 3 $\times $ 2 matrix
$\therefore $ both AB and BA exist and AB is a 2 $\times $ 2 matrix, while BA is a 3 $\times $ 3 matrix
$\therefore \, AB \neq BA$