Addition of Matrices

Addition of Matrices,

Let , and ,

if two matrices are of the same order, & then where , and . For example,

Properties of Matrix Addition

(commutativity of addition)

(associativity of addition)

The associative property of matrix addition can be extend to any finite number of matrices. Besides the parentheses may be omitted also.

Matrix Subtraction

The inverse operation of matrix addition is subtraction. Let the elements of (-A) are the negatives of the corresponding elements of A. The addition is then

Therefore the identity under matrix addition is the zero matrix, that is

Scalar Multiplication

The multiplication of a matrix by a scalar k is

where every element of A is multiplied by the scalar k is,