Question

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

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

Answer 1

Answer: (A)

$3\times 4$

Order of $A$ is $3X4.$

Order of $A^T$ is $4X3$

Since $A^{T}B,$ is defined. So, B must have 3 rows.

Also, $B{A}^T$ is defined. So, B must have 4 columns
Order of $B$ is $3X4$