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. $2\times 2$

Answer 1

The correct option is C $3\times 2$

When a matrix of order $m\times a$ is multiplied with another matrix of order $a\times n$, the resulting product matrix is of the order $m\times n$
Te product of two matrices of the order $2\times 2$ and of order $2\times 3$, will be of the order $2\times 3$
Now, as M is multiplied with a matrix of order $2\times 3$ we have $a=2,n=3$
And as the resulting product matrix is a square matrix, M should be of the order $3\times 2$