Question

If order of matrix $A$ is $4\times 3$ and order of matrix $B$ is $3\times 5$ then order of matrix $B^{\prime }{A}^{\prime }$ is:

• A. $5\times 2$
• B. $4\times 5$
• C. $5\times 4$
• D. $3\times 2$

Answer 1

Answer: (C)

$5\times 4$

Order of matrix $A=4\times 3\left(\text{Given}\right)$

$\therefore$ Order of matrix $A^{\prime }=3\times 4$

Order of matrix $B=3\times 5\left(\text{Given}\right)$

$\therefore$ Order of matrix $B^{\prime }=5\times 3$

Number of rows in $A^{\prime }$ is equal to the number of columns in $B^{\prime }$, i.e., $3$

Therefore,

${\left[B^{\prime }\right]}_{5\times 3}\times {\left[A^{\prime }\right]}_{3\times 4}={\left[AB\right]}_{5\times 4}$

Hence the order of matrix $B^{\prime }{A}^{\prime }$ is $5\times 4$.