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Homework Statement
Let R be the ring of all 2*2 matrices over Zp, p a prime,. Show that if det(a b c d) = ad - bc ≠ 0, then (a b c d) is invertible in R.
Homework Equations
The Attempt at a Solution
I don't know how to start if Zp, with p a prime, is the clause. I know that since ad- bc ≠ 0, it automatically makes the matrix (a b c d) invertible in R.. but does the determinant have to be one?
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