Skip to main content

Algebra of Matrices (2D Arrays) Part II

As you know from the previous article, matrices are 2D arrays. In the previous article, we saw how two matrices are added and subtracted. In this article, we will continue our discussion on algebra of two matrices by discussing how two matrices are multiplied.

Multiplication of two Matrices

Multiplication of two matrices mat1[a x b] and mat2[p x q] is only valid if b=p. While there are many algorithms by which two matrices can be multiplied, here I’ll give you the most simple algorithm. Others are used when efficiency matters.

Algorithm for Multiplication of two Matrices


  • Two 2D arrays to be mat1 [p][p] and mat2 [p][p] having same number of rows and columns.

  • A third 2D array, mul [p][p] to store the result.

Here is the algorithm:

  1. FOR I = 0 TO (p-1)
  2. FOR J = 0 TO (p-1)
         mul [I][J] = 0
         FOR K = 0 TO (p-1)
         mul [I][J] += (mat1 [I][K] * mat2 [K][J])

Below is a example program which illustrates the multiplication of two matrices by this algorithm:

  // Example program in C++
  // It shows you how to
  // multiply two matrices

  void main(void)
   int i,j,k;
   // this constant determines
   // the number of rows and columns
   const int max=3;

   int mat1[max][max];
   int mat2[max][max];
   int mul[max][max];

   cout<<"enter elements for mat1:";

   cout<<"enter elements for mat2:";

   // multiplication of two matrices
   // is done here
   // till here

   // show the contents of the array
   // after formatting
       cout<<mul[i][j]<<" ";


Related Articles:

Popular posts from this blog

Fix For Toshiba Satellite "RTC Battery is Low" Error (with Pictures)

RTC Battery is Low Error on a Toshiba Satellite laptop "RTC Battery is Low..." An error message flashing while you try to boot your laptop is enough to panic many people. But worry not! "RTC Battery" stands for Real-Time Clock battery which almost all laptops and PCs have on their motherboard to power the clock and sometimes to also keep the CMOS settings from getting erased while the system is switched off.  It is not uncommon for these batteries to last for years before requiring a replacement as the clock consumes very less power. And contrary to what some people tell you - they are not rechargeable or getting charged while your computer or laptop is running. In this article, we'll learn everything about RTC batteries and how to fix the error on your Toshiba Satellite laptop. What is an RTC Battery? RTC or CMOS batteries are small coin-shaped lithium batteries with a 3-volts output. Most laptops use

The Best Way(s) to Comment out PHP/HTML Code

PHP supports various styles of comments. Please check the following example: <?php // Single line comment code (); # Single line Comment code2 (); /* Multi Line comment code(); The code inside doesn't run */ // /* This doesn NOT start a multi-line comment block /* Multi line comment block The following line still ends the multi-line comment block //*/ The " # " comment style, though, is rarely used. Do note, in the example, that anything (even a multi-block comment /* ) after a " // " or " # " is a comment, and /* */ around any single-line comment overrides it. This information will come in handy when we learn about some neat tricks next. Comment out PHP Code Blocks Check the following code <?php //* Toggle line if ( 1 ) {      // } else {      // } //*/ //* Toggle line if ( 2 ) {      // } else {      // } //*/ Now see how easy it is to toggle a part of PHP code by just removing or adding a single " / " from th

How to Remove Bullet Points in CSS

This will be a short guide on how to remove bullet points from ordered/unordered lists with CSS, you only need two lines of CSS for this. The first removes the actual bullet points and the second one removes the space to the left, as evident from the following video: We'll also be doing some bullet beautification in the last section if that's what you are looking to do. How to Remove Bullet Points in HTML/CSS Now that we know what CSS properties actually accomplish what we want let's see how we can implement this in our HTML code. Using Inline "style" Tag (The quick and dirty way) As the title suggests, this is the quickest way to remove bullet points in which you wouldn't have to edit any CSS files (for example, for Blogger or WordPress). This method would be useful for a one-off case - just add the following " style " attribute to the list you want to remove the bullet points from: <h1>Ordered List</h1> <ol  style="list-styl