Question

If $A$ is an $m\times n$ matrix such that $AB$ and $BA$ are both defined, then order of $B$ is

• A. $m\times n$
• B. $n\times m$
• C. $n\times n$
• D. $m\times m$

Answer 1

The correct option is B $n\times m$

Since $AB$ exists, so the number of column in $A=$ Number of column in $B$.

So $B$ has $n$ row.

Since $BA$ exists, so the number of column in $B=$ Number of column in $A$.

So $B$ has $m$ column.

$\therefore$ B is an $n\times m$ matrix.