Question

Two matrices $A=[a_{ij}{]}_{p\times q},B=[b_{ij}{]}_{m\times n}$ are equal if.

• A. p=n, q=m and $a_{ij}=b_{ij}\forall i,j$
• B. $p=m,q=n$
• C. p=m, q=n and $a_{ij}=b_{ij}\forall i,j$
• D. None of these

Answer 1

The correct option is C

p=m, q=n and $a_{ij}=b_{ij}\forall i,j$

The matrixes can be equal only if their orders are identical and also their corresponding elements should be same.

$eg.\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]\&\left[\begin{array}{cc}1& 3\\ 2& 4\end{array}\right]AB$

are not equal matrixes because though their orders are same and the matrixes are made of same elements. Still if you observe carefully that $a_{12}\ne b_{12}and{a}_{21}\ne b_{21}$. So, they are not equal.

So option C is correct