Matrices are commonly used to encrypt data. Here is a simple form such an encryption can take. First, we represent each letter in the alphabet by a number, so let us take  = 0, A = 1, B = 2, and so...

Matrices are commonly used to encrypt data. Here is a simple form such an encryption can take. First, we represent each letter in the alphabet by a number, so let us take < space > = 0,A = 1,B = 2, and so on. Thus, for example, "ABORT MISSION" becomes

To encrypt this coded phrase, we use an invertible matrix of any size with integer entries. For instance, let us takeA to be the 2 × 2 matrix

 We can first arrange the coded sequence of numbers in the form of a matrix with two rows (using zero in the last place if we have an odd number of characters) and then multiply on the left byA.

which we can also write as

To decipher the encoded message, multiply the encrypted matrix by

 The following exercise uses the above matrixA for encoding and decoding.


Use the matrixA to encode the phrase "GO TO PLAN B".