# Numerical Methods: Multiplication of two matrices using two dimensional array in C

Let we have two 2 x 2 matrices A and B

Let we have two 2 x 2 matrices A and B
$A = \begin{bmatrix} a_{00} & a_{01}\\ a_{10} & a_{11} \end{bmatrix} \text{ and } B = \begin{bmatrix} b_{00} & b_{01} \\ b_{10} & b_{11} \end{bmatrix}$
The multiplication of $A$ and $B$ works as follows

1. Multiply $a_{00}$ with $b_{00}$ and $a_{01}$ with $b_{10}$ and sum them together. So the first element $r_{00}$ becomes  $a_{00}$ . $b_{00}$ + $a_{01}$ . $b_{10}$
2. Multiply $a_{00}$ with $b_{01}$ and $a_{01}$ with $b_{11}$ and sum them together. So the first element $r_{01}$ becomes  $a_{00}$ . $b_{01}$ + $a_{01}$ . $b_{11}$
3. Multiply $a_{10}$ with $b_{00}$ and $a_{11}$ with $b_{10}$ and sum them together. So the first element $r_{10}$ becomes  $a_{10}$ . $b_{00}$ + $a_{11}$ . $b_{10}$
4. Multiply $a_{10}$ with $b_{01}$ and $a_{11}$ with $b_{11}$ and sum them together. So the first element $r_{11}$ becomes  $a_{10}$ . $b_{01}$ + $a_{11}$ . $b_{11}$
So the resulting matrix $R$ becomes,
$R = \begin{bmatrix} a_{00}.b_{00}+a_{01}.b_{10} & a_{00}.b_{01} + a_{01}.b_{11} \\ a_{10}.b_{00} + a_{11}.b_{10} & a_{10}.b_{01} + a_{11}.b_{11}\end{bmatrix}$
Note: In order to multiply two matrices, $A$ and $B$, the number of columns in $A$ must equal the number of rows in $B$. Thus, if $A$ is an $m * n$ matrix and $B$ is an $r * s$ matrix, $n = r$.

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### 6 Responses

1. Shayan Ahmed says:

this is wrong…. the multiplication logic is not right….

2. Bibek Subedi says:

Shayan thanks for reply … but i don't think the logic is wrong. Can you prove it?

3. Marouf says:

Bibek, your code for Marixmultiplication is korekt and gut, may be mohr in analytical Geometry source code in c/c++

4. Marouf says:

I think your source code in c/c++ for two Matrix multiplication is correct and not wrong, which Mr Shayan mean, thank you for very nice and in simply way to write your programm about numerical Mathematic, i hope more in analytical Geometrie like point,victor,line,plan in c/c++, my compiler is dev c++ from blood sheet

5. Varinder Singh says:

its not c++ its c..

6. Sanjay says:

Its wrong. 