Addition and Subtraction of Matrices

When can two matrices be added or subtracted?

Two matrices can be added or subtracted only if they are of the SAME order — this requirement is called being conformable for addition/subtraction. It is meaningless, for instance, to add a $2\times2$ matrix to a $2\times1$ matrix.

The rule

When two matrices $A$ and $B$ are of the same order, their sum $A+B$ (or difference $A-B$) is found by adding (or subtracting) each pair of CORRESPONDING elements — the element in a given row and column of the answer comes only from the elements in that SAME row and column of $A$ and $B$:

Subtraction follows exactly the same element-by-element pattern, with each $+$ replaced by $-$.