Equal Matrices | Matrices

Two matrices A and B are said to be equal if,

1. They have same order, and
2. Corresponding elements of A are equal to elements of B,

i.e. $A_{ij} = B_{ij}$, for all i,j.

Example:

A = $\begin{bmatrix}1 & 2\\3 & 4\end{bmatrix}$ and B = $\begin{bmatrix}1 & 2\\4 & 3\end{bmatrix}$

are not equal, because $A_{21}$ = 3 $\neq$ $B_{21}$ = 4.

Hence for two matrices to be equal, all elements should be equal at the exact location ($A_{ij}$).