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 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

The correct option is B $AB,BA$ exist and are not equal

Since, we have $A=2\times 3,B=3\times 2$

So, both $AB$ and $BA$ exist.
But both are not equal to each other because bith are if different order

$\because AB\to 2\times 2$ and $BA\to 3\times 3.$