Question

Given $A$ is a matrix of order $3\times 2$. If order of $AB$ is $3\times 3$, then order of $B$ will be

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

Answer 1

The correct option is B $2\times 3$

Given $A$ is a matrix of order $3\times 2$.

Now $AB$ is of order $3\times 3$.

The product $AB$ is possible if the number of columns of $A(=2)$ is equal to the number of rows of $B$.

Since order of $AB$ is $3\times 3$.

Also the number of columns of $B$ is same as the number of columns of $AB$.

Now $A$ is of order $2\times 3$.