Two matrices $A$ and $B$ are said to be equal if both of the following conditions hold:

• $A$ and $B$ have the same size; and
• every entry of $A$ is equal to the corresponding entry of $B$; in other words, for every $(i,j)$ so that $A$ and $B$ have an $(i,j)$ entry, we have $a_{ij}=b_{ij}$.

When $A$ and $B$ are equal matrices, we write $A=B$. Otherwise, we write $A\ne B$.