## Scalar Multiple of a Matrix

When we multiply a real number with a matrix , we have the scalar multiple of . The scalar multiple matrix has the same size of the input matrix and it is obtained by multiplying each element of by that is .

Example

The interactive program below shows you the result of matrix scalar multiple. Your input is a matrix of any size but less than 100 scalar elements and a scalar number. Random Example will generate both random matrix and random scalar.

Matrix A = scalar k =

## Properties

Some important properties of matrix scalar multiple are

• Matrix scalar multiple is a commutative operation. When the order is reversed, you will still get the same result
• Matrix scalar multiple is an associative operation. You can exchange the order of computation (operation inside parentheses are to be computed first) does not change the result .
• Matrix scalar multiple is a distributive operation. You can distribute (and group) the scalar with respect to addition and multiplication .
• Matrix scalar multiple is also an associative operation with respect to matrix product . You can exchange the order of computation (operation inside parentheses are to be computed first) does not change the result .
• When the scalar is zero, matrix scalar multiple will produce a zero matrix
• When the scalar is one, matrix scalar multiple will produce the input matrix itself
• When the scalar is negative one, matrix scalar multiple will produce the negative of the input matrix