Question

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

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

Answer 1

Answer: (D)

$3\times 4$

For $A{B}^T$ and $B^{T}A$ to exist

$B^T$ must be of the order $4\times 3$ as A is of the order $3\times 4$
Therefore $B$ is of the order $3\times 4$
Ans: D