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Justabeginner
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Homework Statement
Let R be the ring of all 2*2 matrices, over Zp, p a prime. Let G be the set of elements x in the ring R such that det x ≠ 0. Prove that G is a group.
Homework Equations
Matrix is invertible in ring R.
The Attempt at a Solution
Group properties and ring properties are similar I think.
Group and Ring - closure, associativity, identity (zero in Rings?)
Is this how I am supposed to approach the problem? By proving the common properties of a group and ring?