Secret Codes With Matrices

Matrix multiplication can be used to encode and decode messages.

To encode a message:

Translate each letter in your message into a number (A=1, B=2, C=3, space=0). For example:

BEETLE becomes 2 - 5 - 5 - 20 - 12 - 5

Put the numbers into a 3x2 matrix:

Multiply our encoding matrix by this matrix:

Add or subtract 26 from each number in the new matrix until the result is between 0 and 26. For example:

And finally, translate these numbers back into letters:

To decode a message:

Translate letters to numbers and put them back into a 3x2 matrix:

Multiply our decoding matrix by this matrix:

Add or subtract 26 from each number in the new matrix until the result is between 0 and 26:

And finally, translate these numbers back into letters: