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).

hello :

by applying the distributive property :

6 × 4.3 = 6 × ( 4 + 0.3 )

            =   (6 ×   4) + (6 ×   0.3)

            = 24 + 1.8

6 × 4.3 = 25.8

here is a big fat