2.1 Matrix Equality

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.