Matrix Multiplication:

The Matrix multiplication does not mean multiplying term by term; and it is not an array operation. The Matrix multiplication has a very particular meaning. First of all, in order to multiply a matrix A by a matrix B to answer in a matrix C, the number of columns of A should be similar to the number of rows of B. If the matrix A has dimensions m × n that means that matrix B should have dimensions n × something; and we'll call it p. We say that the inner dimensions should be similar. The resultant matrix C has similar number of rows as A and similar number of columns as B (in another words, the outer dimensions m × p). In mathematical notation, [A]_{m x n} [B]_{n x p} = [C]_{m x p}. This only defines the size of C.

The elements of the matrix C are defined as the addition of products of corresponding elements in the rows of A and columns of B, or in another words

In the example below, A is 2 × 3 and B is 3 × 4 therefore C will be 2 × 4. The elements in C are acquired by using the summation. The first row of C is obtained by using the first row of A and in succession the columns of B. For illustration, C(1,1) is 3 * 1 +  8 * 4  + 0 * 0 or 35. C(1,2) is 3 * 2  + 8 * 5  + 0 *2 or 46.