# 2.1 Matrix Equality

Two m × n matrices A and B are equal if their corresponding elements are equal.

 $\mathbf{A=B}$ (4)

implies

 $a_{ij}=b_{ij},\operatorname{where}1\leq i\leq m\operatorname{and}1\leq j\leq n$ (5)

The notion of matrix equality is undefined unless the operands have the same dimensions.