q show matrix multiplication problemlet there be

Question

Q. Show Matrix Multiplication Problem?

Let there be 2 matrices M1 and M2 of sizes a x b and b x c correspondingly. If we multiply M1 and M2 product matrix O will be of size a x c. 

The values of elements which are stored in the matrix O are in proportion to the subsequent formula:

       O_ij = Summation x of (M1_ix * M2_xj) x=1 to b, where 1

Remember for multiplying a matrix M1 with other matrix M2 number of columns in M1 should be equal to number of rows in M2. The renowned matrix multiplication algorithm on sequential computers occupies O(n³) running time. For multiplication of two 2x2 matrices the algorithm needs 8 multiplication and 4 addition operations. One other algorithm known as Strassen algorithm has been worked out that requires 7 multiplication and 14 addition or subtraction operations. Time complexity of Strassen's algorithm is O(n^2.81). The fundamental sequential algorithm is explained below:

Algorithm: Matrix Multiplication

Input// Two Matrices M1 and M2

 For I=1 to n

      For j=1 to n

        {

               O_ij = 0;

               For k=1 to n

                    O_ij= O_ij + M1_ik * M2_kj

               End For

       } 

      End For 

End For