How to Multiply Two Matrices

There are two easy steps for multiplying two matrices with each other .  First steps tells you the main condition which you have to check yourself and second step will tell you how practical we can multiply two matrices .


  First Step 

In First
We can multiply to matrix , if the number of column of first matrix will equal to the number of rows of second matrix .

Suppose first matrix is A and second matrix is B

              4     5                         6    5    4 
  A =                            B = 
              6     7                        2      3    1

rows and column of A = 2             and  rows of B matrix is = 2 and column of B matrix is = 3

Because number of column of first matrix is 2 which is equal to the number of rows of second matrix B .

So , A can multiply with B

   Second  Step   

After  clearing first step  , we will reach second step , in second step we will learn how can multiply matrix each element with other matrix's element .

We multiply every row with other matrix's column .

Suppose in above example

First element after multiply  → first row A  is  4 and 5  and first column of  B is  6 and 2
Second element will be on first row and second columm  →  first row A is 4 and 5 and second column of B is 5 and 3
Now
We will find third element which will be on first row and  third column → first row A is 4 and 5 and third column of B  4 and 1
Now same way we will find second row after multiply A and B which will be three column


Write

                      4 x 6 + 5 x 2       4 x 5 + 5 x 3          4 x 4 + 5 x 1


A X B = 

                        6 x 6 +7 x 2        6 x 5 + 7 x 3          6 x 4 + 6 x 1


After this  multiply and add with each other 


             34           35           21
AB = 
           
             50             51          30