# Invertible Matrix

• Jan 14th 2007, 12:01 PM
thesummerofgeorge
Invertible Matrix
I need to find the relationship between the number of 2 x 2 matrices and the number of invertible 2 x 2 matrices over Zp where p is a prime number.

To help me, I took Z2 because 2 is a prime number. There appear to be 2^4=16 different matrices over Z2. Is this right?

Of these, I found 6 of them to be invertible.

Therefore, I think that the number of matrices is p^4. But I don't know the relationship between p and the number of invertible matrices. What is this?

Thank you.
• Jan 14th 2007, 01:40 PM
ThePerfectHacker
Quote:

Originally Posted by thesummerofgeorge
I need to find the relationship between the number of 2 x 2 matrices and the number of invertible 2 x 2 matrices over Zp where p is a prime number.

To help me, I took Z2 because 2 is a prime number. There appear to be 2^4=16 different matrices over Z2. Is this right?

Of these, I found 6 of them to be invertible.

Therefore, I think that the number of matrices is p^4. But I don't know the relationship between p and the number of invertible matrices. What is this?

Thank you.

Look here.
http://www.mathhelpforum.com/math-he...=Algebra+units