Question

The order of the matrix $A$ is $3\times 5$ and that of $B$ is $2\times 3$. The order of the matrix $BA$ is:

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

Answer 1

Answer: (C)

$2\times 5$

$Theory:$ Two matrices are said to be conformable for multiplication if the number of columns in prefactor is equal to the number of rows in the post factor. The order of the resultant matrix is the number of rows in prefactor matrix times the number of columns in the post factor matrix

i.e., if $A=[a_{ij}{]}_{n\times m}$ and $B=[b_{jk}{]}_{p\times n}$

Then, multiplication of the matrices $[B{]}_{p\times n}\times [A{]}_{n\times m}$ results in matrix $[BA{]}_{p\times m}$.

Given, $[A{]}_{3\times 5}$ and $[B{]}_{2\times 3}$

Hence, order of the matix $\left[BA\right]$ is $2\times 5$