Gl (n, r), the set of invertible nxn matrices with real entries, is a group under matrix multiplication. determine if the nxn matrices with determinant -1 or 1 is a subgroup. if not, which property does not hold?

Let

The subset S is a subgroup of GL(n,R) if satisfies:

1. The identity matrix belong to S.

2. If A and B are in S then AB is in S.

3. If A is belong to S then belongs to S.

Let's see if S satisfies these conditions.

1.  We know that , then .

2. Let A and B in S.

Then AB is in S.

3. Let , , then .

Since S satisfies all conditions then S is a subgroup of GL(n,R).

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