LInear algebra coding question

[Mdhiggenz]

Homework Statement

Describe how to create a coding matrix A so that A^-1
has no fractions

The answer is Multiply a few type III matrices together, so that det A = 1

What I put is to just use an upper triangular matrix, since the det of an upper triangular matrix is 1 and you have to do row operations in order to get the matrix into an upper triangular form.

Not sure if answer would be accepted as partially correct.

Homework Equations

The Attempt at a Solution

 

[STEMucator]

Presuming you're working your matrix over the integers, it's easy to create an encrypting matrix so that its decoding matrix will have no fractions in it.

You're correct for the case of 2x2 matrices, as long as ad-bc = 1, you're good to go. I'm not sure for the general nxn case though.