SCALAR MULTIPLE: Given any matrix , we can define the scalar multiple with scalar . For example,
SUM: Given two matrices and , we can define the sum of matrix. For example,
MATRIX MULTIPLICATION: Given matrix and matrix , we can define the multiplication of matrix. Suppose, for example, that we have a matrix and a matrix . Then we can compute the multiplication of matrix by
The matrix multiplication is not commutative. That is, in general.