A **matrix** is said to be as ordered rectangular array of number. The operation on matrices that is the multiplication of a matrix generally falls into two categories

- Scalar Multiplication: In the matrix, a real number is called a scalar in which a single number is being multiplied by all the elements present in the matrix.
- Multiplication of the matrix with another entire matrix.

**Scalar Multiplication**

Multiplication of scalar means, multiplying a matrix by a number i.e. a real number. In general, we may define multiplication of a matrix by a scalar as follows: If is a matrix and k is a scalar, then kA is another matrix which is obtained by multiplying each element of A by the scalar number k. In other words, that is, (i,j) element of kA is for all possible values of i and j.

### Properties of multiplication of matrices

**The associative law:**For any three matrices A, B and C. We have (AB)C =A(BC), whenever both sides of the equality are defined.**The distributed law:**For three matrices A, B and C. (i) A (B+C) = AB + AC and (ii) (A+B)C = AC + BC, whenever both sides of equality are defined.**The existence of multiplicative identity:**For every square matrix A, there exists an identity matrix of same order such that IA = AI = A.

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