By multiplying a matrix A of dimensions R and C with a matrix B of dimensions C and P, a matrix MULT of dimensions R and P is obtained:
A (R, C) * B (C, P) = MULT (R, P)

The multiplication of two matrices is done by multiplying the components of the two matrices rows by columns:

\(MULT_{ij}=(\sum_{k=1}^{C}a_{ik}\times b_{kj})\)

Write a program that performs the multiplication of two matrices A and B. The result of the multiplication will be stored in a third matrix MULT which will then be displayed.

\(\begin{pmatrix} a & b & c  \\e & f & g  \\ h & i & j \\ h & l & m \end{pmatrix} \times \begin{pmatrix} p & q \\ r &s \\ t & u \end{pmatrix} = \begin{pmatrix} a \times p + b \times r + c \times t  &     a \times q + b \times s + c \times u  \\ e \times p + f \times r + g \times t   &   e \times q + f \times s + g \times u   \\ h \times p + i \times r + j \times t    &  h \times q + i \times s + j \times u   \\ k \times p + l \times r + m \times t   &   k \times q + l \times s + m \times u \end{pmatrix}\)

#include <stdio.h>
#include <conio.h>
#define SIZE 50
main()
{
	int A[SIZE][SIZE];  
	int B[SIZE][SIZE];  
	int MULT[SIZE][SIZE];  
	int R, C, P;   
	int I, J, K;    



	printf("*** Matrix A ***\n");

	do {
		printf("Number of rows of    A (max.%d) : ", SIZE);
		scanf("%d", &R);
	} while (R <= 0 || R > SIZE);
	do {
		printf("Number of columns of A (max.%d) : ", SIZE);
		scanf("%d", &C);
	} while (C <= 0 || C > SIZE);

	for (I = 0; I<R; I++)
		for (J = 0; J<C; J++)
		{
			printf("A[%d][%d] : ", I, J);
			scanf("%d", &A[I][J]);
		}

	printf("*** Matrix B ***\n");
	printf("Number of rows of    B : %d\n", C);
	printf("Number of columns of B (max.%d) : ", SIZE);
	scanf("%d", &P);
	for (I = 0; I<C; I++)
		for (J = 0; J<P; J++)
		{
			printf("B[%d][%d] : ", I, J);
			scanf("%d", &B[I][J]);
		}


	printf("Matrix A :\n");
	for (I = 0; I<R; I++)
	{
		for (J = 0; J<C; J++)
			printf("%7d", A[I][J]);
		printf("\n");
	}

	printf("Matrix B :\n");
	for (I = 0; I<C; I++)
	{
		for (J = 0; J<P; J++)
			printf("%7d", B[I][J]);
		printf("\n");
	}

	/* Multiplication */
	for (I = 0; I<R; I++)
		for (J = 0; J<P; J++)
		{
			MULT[I][J] = 0;
			for (K = 0; K<C; K++)
				MULT[I][J] += A[I][K] * B[K][J];
		}


	printf("Resultant matrix :\n");
	for (I = 0; I<R; I++)
	{
		for (J = 0; J<P; J++)
			printf("%7d", MULT[I][J]);
		printf("\n");
	}
	getch();
}