The sum of m × n matrices A and B is an m × n matrix C which is the element by element sum of the addends.
C = A + B
cij = aij + bij, where 1 ≤ i ≤ m and 1 ≤ j ≤ n
Matrix addition is undefined unless the addends have the same dimensions. Matrix addition is commutative.
A + B = B + A
Matrix addition is also associative.
(A + B) + C = A + (B + C)
The additive identity is the zero matrix. The additive inverse of matrix A is denoted by –A and consists of the element by element negation of a A, i.e. it’s the matrix formed when a A is multiplied by the scalar –1.
–A = –1 · A