Order of the matrices must be the same
Add corresponding elements together
Matrix addition is commutative
Matrix addition is associativ
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:
Matrix of any order
Consists of all zeros
Denoted by capital O
Additive Identity for matrices
Any matrix plus the zero matrix is the original matrix