Question

$M\times \left(\begin{array}{cc}1& 2\\ 0& 5\end{array}\right)\left(\begin{array}{ccc}2& 3& 0\\ 4& -2& 1\end{array}\right)$ is a square matrix, then the order of M is

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

Answer 1

The correct option is C $3\times 2$

$M\times \left[\begin{array}{cc}1& 2\\ 0& 5\end{array}\right]\left[\begin{array}{ccc}2& 3& 0\\ 4& -2& 1\end{array}\right]$

Let mxn be the order of matrix M$M_{(m\times n)}\times \left(A_{(2\times 2)}{B}_{(2\times 3)}\right)$

For multiplication of two matrices to be possible the columns of first matrix should be equal to the number of rows of second matrix

Also the order of result matrix of say example $A_{m\times n}$ and

$B_{p\times q}$

For AB it is mxq and BA it is pxn

Now, order of resultant of $A_{(2\times 2)}{B}_{(2\times 3)}$

is say $C_{(2\times 3)}$

$M_{(m\times n)}{C}_{(2\times 3)}$ clearly $n=2$

Resultant of $M_{(m\times n)}{C}_{(2\times 3)}$

$=N_{(m\times 3)}$

Given N is square matrix

$\Rightarrow m=3$

$\therefore$ Order of M is $(3\times 2)$