Two m × n matrices A and B are equal if their corresponding elements are equal.
| $$\mathbf{A=B}$$ | (4) |
implies
| $$a_{ij}=b_{ij},\mbox{ where }1 \leq i \leq m \mbox{ and }1 \leq j \leq n$$ | (5) |
The notion of matrix equality is undefined unless the operands have the same dimensions.