Question

If $A=\left[\begin{array}{ccc}1& -2& 3\\ -4& 2& 5\end{array}\right]$ and $B=\left[\begin{array}{cc}2& 3\\ 4& 5\\ 2& 1\end{array}\right]$, 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
$\therefore AB\ne BA$