How to multiply the matrix

Matrix multiplication requires a certain condition: the number of columns of the first matrix multiplier must be equal to the number of rows of the second. In addition, this operation is not commutative, that is, the result depends on the order of the factors.

Instruction

1. By definition, the matrix C, the product of matrices A and B consists of elements[i,j], each of which is equal to the sum of products of elements of row i of the matrix A by the corresponding elements of column j of matrix B. This can be written by formula. The formula takes into account that the matrix A has dimension m x p and matrix B is p x n. Then the matrix C will have the dimension m x n.
2. Let's consider an example. Multiply the matrices A and B indicated in the figure. Consistently we find all the elements of the matrix C = AB.
   [1,1] = a[1,1]*b[1,1] + a[1,2]*b[2,1] + a[1,3]*b[3,1] = 3*2 + 2*5 + 0*3 = 16
   c[1,2] = a[1,1]*b[1,2] + a[1,2]*b[2,2] + a[1,3]*b[3,2] = 3*1 + 2*4 + 0*2 = 11
   c[2,1] = a[2,1]*b[1,1] + a[2,2]*b[2,1] + a[2,3]*b[3,1] = 1*2 + 3*5 + 1*3 = 20
   c[2,2] = a[2,1]*b[1,2] + a[2,2]*b[2,2] + a[2,3]*b[3,2] = 1*1 + 3*4 + 1*2 = 15