Matrix addition, Properties, Examples, Solved Exercises

Addition

Properties of Matrices

Property

Commutativity of Addition

Associativity of Addition

Opposite 

Example

A + B = B + A

A + ( B + C ) = ( A + B ) + C

A + ( - B ) = A - B

The usual matrix addition is defined for two matrices of the same dimensions. The sum of two m × n (pronounced "m by n") matrices A and B, denoted by A + B, is again an m × n matrix computed by adding corresponding elements:

For example:

We can also subtract one matrix from another, as long as they have the same dimensions. A − B is computed by subtracting corresponding elements of A and B, and has the same dimensions as A and B. For example:

Zero Matrix