Question

If $A$ is $3\times 4$ matrix and B is a matrix such that $A^{T}B$ and $B{A}^T$ are both defined, then $B$ is of order

• A. $3\times 4$
• B. $3\times 3$
• C. $4\times 4$
• D. $4\times 3$

Answer 1

Answer: (A)

$3\times 4$

Since, $A$ is of order $3\times 4$.

Thus, order of $A^T=4\times 3$

Now, let $B$ has order $=m\times n$

For $A^{T}B$ to be defined, we must have $3=m$ and for $B{A}^T$ to be defined, $n=4$

So, order of $B=m\times n=3\times 4$