Q.Two matrices are equal if they have same number of rows and same number of columns.

Equal order (same number of rows and same number of columns) is necessary but not sufficient. Two matrices are equal only if they have the same order and every corresponding entry matches: $a_{ij}=b_{ij}$ for all $i,j$. …

The statement

It says two matrices are equal if they have the same number of rows and columns. That is only half of the definition.

The correct definition

Two matrices $A=[a_{ij}]$ and $B=[b_{ij}]$ are equal when

1. they have the same order (same number of rows and same number of columns), and
2. every corresponding entry is equal: $a_{ij}=b_{ij}$ for all $i,j$.

A counterexample

$A=\begin{bmatrix}1&2\\3&4\end{bmatrix},\qquad B=\begin{bmatrix}1&0\\3&4\end{bmatrix}.$ …

Method: Apply the full definition of matrix equality

Use this to judge statements about when two matrices are equal.

Steps

Step 1: State both requirements.

Matrices $A$ and $B$ are equal iff (i) they have the same order, and (ii) every corresponding entry is equal: $a_{ij} = b_{ij}$ for all $i,j$.

Step 2: Test whether the claim captures both. …

Common Mistakes

Mistake 1: Believing equal order is sufficient for equality.

Why it's wrong: same order is necessary but not sufficient — the entries must match too. Correct approach: check every corresponding entry, e.g. $\begin{bmatrix}1&2\\3&4\end{bmatrix} \neq \begin{bmatrix}1&0\\3&4\end{bmatrix}$ despite equal order. …