$A=1,B=2,$ and so on$.$ Thus, for example, "ABORT MISSION" becomes

$\left[\begin{array}{ccccccccccccc}1& 2& 15& 18& 20& 0& 13& 9& 19& 19& 9& 15& 14\end{array}\right].$

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

$22$ matrix $\left[\begin{array}{cc}3& 4\\ 1& 2\end{array}\right].$

Encrypted Matrix $=\left[\begin{array}{ccc}3& 4& 2\end{array}\right]$

$1\left[\begin{array}{ccccccccccccc}1& 15& 20& 13& 19& 9& 14& 18& 0& 2& 19& 15& 0\end{array}\right]$

$2$

$=\left[\begin{array}{ccccccccccccc}11& 117& 60& 75& 133& 87& 42& 51& 20& 31& 57& 39& 14\end{array}\right]$

$5$

which we can also write as

$\left[\begin{array}{cccccccccccccc}11& 5& 117& 51& 60& 20& 75& 31& 133& 57& 87& 39& 42& 14\end{array}\right].$

To decipher the encoded message, multiply the encrypted matrix by $A^{-1}.$ The following exercise uses the above matrix A for encoding and decoding.

Use the matrix $A$ to encode the phrase $"$GO TO PLAN B$".$