# linear algebra

posted by
**soasi piutau**
.

1)If A is an invertible matrix and k is a positive integer, then

(A^k)^-1 = (A^-1)^k note: ^ stand for power, -1 stand for inverse of A

2)If A is an invertible matrix, then (transpose of A)^-1 =transpose of(A^-1)

3)Prove A^2 = A, then

I - 2A = (I - 2A)^-1 such that A is a Matrix

4)Prove that if A, B, and C are square matrices and ABC = I, then B is invertible and B inverse = CA

5)Prove that if A and B are idempotent and AB = BA then AB is idempotent.

6) Prove that if A is row-equivalent to B, then B is row equivalent to A.

7) Prove that if A is an n x n matrix that is idempotent and invertible, then A = I