There are many ways to encrypt a message. And the use of coding has become particularly significant in recent years (due to the explosion of the internet for example). One way to encrypt or code a message uses matrices and their inverse. Indeed, consider a fixed invertible matrix *A*. Convert the message into a matrix *B* such that *AB* is possible to perform. Send the message generated by *AB*. At the other end, they will need to know *A*^{-1} in order to decrypt or decode the message sent. Indeed, we have

which is the original message. Keep in mind that whenever an undesired intruder finds

**Example.** Consider the matrix

First we keep the first row and add it to the second as well as to the third rows. We obtain

Next we keep the first row again, we add the second to the third, and finally add the last one to the first multiplied by -2. We obtain

This is our matrix

Back to our original problem. Consider the message

To every letter we will associate a number. The easiest way to do that is to associate 0 to a blank or space, 1 to A, 2 to B, etc... Another way is to associate 0 to a blank or space, 1 to A, -1 to B, 2 to C, -2 to D, etc... Let us use the second choice. So our message is given by the string

Now we rearrange these numbers into a matrix

Then we perform the product

The encrypted message to be sent is

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**Author**: M.A. Khamsi

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