Question

If the order of matrices $A$ and $B$ are $3\times 2$ and $2\times 1$ respectively, then find the order of matrix (if possible) $AB$

• A. $1\times 3$
• B. $3\times 1$
• C. $2\times 2$
• D. $2\times 3$

Answer 1

Answer: (B)

$3\times 1$

Order of $A:3\times 2$

Order of $B:2\times 1$

Multiplication of matrices is possible if and only if the number of columns of first matrix is equal to the number of rows of second matrix
In AB

No. of columns in A is $2$

No. of rows in B is $2$

$\therefore$AB exists

Order of AB is ( number of rows of A x number of columns of B)

$\therefore$ Order of AB is $(3\times 1)$