Question

If $A$ is matrix of order $m\times n$ and $B$ is a matrix such that $A{B}^{\prime }$ and $B^{\prime }A$ are both defined, then order of matrix $B$ is

• A. $m\times m$
• B. $n\times n$
• C. $n\times m$
• D. $m\times n$

Answer 1

Answer: (D)

$m\times n$

$A{B}^{\prime }$ is defined only when order of $B^{\prime }$ is $n\times x$

$B^{\prime }A$ is defined only when order of $B^{\prime }$ is $n\times m,i.e.,x=m$

$\therefore$ order of matrix $B$ is $m\times n$