2.1 Matrix Equality

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

𝐀=𝐁\mathbf{A=B} (4)

implies

aij=bij,where1imand1jna_{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.