Question

If $A$ is a $3\times 4$ matrix and $B$ is a matrix such that $A^{\prime }B$ and $B{A}^{\prime }$ are both defined. Then $B$ is of the type

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

Answer 1

The correct option is A $3\times 4$

Since, $A$ is a $3\times 4$ matrix
Order of $A^{\prime }$ is $4\times 3$
Now, since $A^{\prime }B$ exists .
So, $B$ must have $3$ rows
Also, $B{A}^{\prime }$ exists
So, $B$ must have $4$ columns
Hence, order of $B$ is $3\times 4$