Question

If a matrix A is of order $3\times 4$ and there exists a matrix B such that both A'B and BA' are defined. Then the order of B is ____

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

Answer 1

The correct option is A

$3\times 4$

Let order of matrix B be p x q

$A_{3\times 4}\Rightarrow A_{4\times 3}^{\prime }$

Now A'B defined $\Rightarrow B$ is $3\times p$

Again $B_{3\times p}{A}_{4\times 3}^{\prime }$ is defined $\Rightarrow p=4$

​$\therefore B$ is of order $3\times 4$.