Encrypting twice with the same key

From: Daniel Weber (ComeAndSpamIt@gmx.net)
Date: 04/13/03 

From: "Daniel Weber" <ComeAndSpamIt@gmx.net>
Date: Sun, 13 Apr 2003 15:48:53 +0200

Is encrypting twice with the same key safe?
I made up the following:

May f be the encryption transformation, and A be its Matrix with entries
from Z.
f(x) -> Ax

Then encrypting twice would be f(f(x)) = (AA)x = (A^2)x.

Now, there's much lesser possibilities for the entries of A^2.
That would make brute force a better choice.

Did I think right or am I just insane?

Daniel

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