Of course, the sum is the same as the non-zero matrix.

You should be happy with the following rules of matrix addition. In each rule, the matrices are assumed to all have the same dimensions.

**A**+**B**=**B**+**A****A**+**0**=**0**+**A**=**A****0**+**0**=**0**

These look the same as some rules for addition of real numbers.
(**Warning!!** Not all rules for matrix math look the same
as for real number math.)

The first rule says that matrix addition is *commutative*.
This is because ordinary addition is being done on the corresponding
elements of the two matrices, and ordinary (real) addition is
commutative: