Question

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

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

Answer 1

Answer: (A)

$3 \times 4$

Answer 2

Given, $A$ is $3 \times 4$ matrix.
So, $A'$ is $4 \times 3$ matrix.
Since, $A' B$ is defined, therefore $B$ should he $3 \times 4.$
Also, $B A'$ is defined, so $B$ should be $3 \times 4$.
Hence, $B$ is of the type $3 \times 4$