Decoding a matrix encryption cipher

[Dooga Blackrazor]

http://www.sosmath.com/matrix/coding/coding.html

How would you decode the encryption at the bottom of the page?

 

[Diane_]

Find the inverse of A and left-multiply it by the coded matrix. Call B the message matrix, and B' the coded matrix. You get the coded matrix by finding

AB = B'

Get the uncoded matrix by taking

A^(-1)B' = A^(-1)AB = IB = B

 

[shmoe]

They give the inverse matrix of A just above the sentence "I LOVE MONICA". It appears to be off though, and is actually the negative of the inverse.