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

$m \times n$

The correct answer is Option (4) → $m \times n$ ##

Let $A = [a_{ij}]_{m \times n} \text{ and } B = [b_{ij}]_{p \times q}$

$∴$ $B' = [b_{ji}]_{q \times p}$

Now, since $AB'$ is defined, so $n = q$

and $B'A$ is also defined, so $p = m$

$∴$ Order of $B' = [b_{ji}]_{n \times m}$

So, Order of $B = [b_{ij}]_{m \times n}$