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Let x = [aij],                          I = 1, 2, …, r; j = 1, 2, ….s,

and, y = [bjk],                       j = 1, 2, …., p; k = 1, 2, ….,q

be two r × s and p × q matrices in that order such that the number of rows of B is the similar as the number of columns of A.

After that the product of these two matrices is classified as an r × q matrix C = AB = [cik], I = 1, …., r; k = 1, …,qp

here cik = ai1 b1k + ai2 b2k + ….. + ain bnk = bik

= Sum of the products of the factors of ith row and jth columns of A with the equivalent elements of jth row and kth columns of B.

Reminder: cik is found by multiplying the elements in the ith row of A with the equivalent elements in the kth column of B and then adding them.

The product matrix AB will contain r rows and q columns, i.e. if A is an r × q matrix and B is s × q matrix, after that AB is an r × q matrix.

In the product AB, A is well-known pre-factor and B as post-factor.

Therefore we notice that the product AB is defined if and only if numerous columns of the pre-factor is equal to the number of rows of the post-factor.

Two matrices A and B are said to be contented for multiplication if the number of columns of A is equal to the number of rows of B.

Reminder: It is significant to note that there can be matrices which are not contented for multiplication and in that case we state that the multiplication of the matrices is not distinct. We consider a few instances to illustrate the above data.
Matrix Scalar Multiplication
The scalar multiple kA of a matrix A (square or rectangular) through a scalar k is a matrix obtained by multiplying each element of A by the scalar k.

For instance: the scalar multiple of the matrix A by k.

Negative of a matrix: The negative of a matrix A is – A.

We portray – A = (–1) A

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