Homework Help: linear algebra

Posted by soasi piutau on Friday, April 13, 2012 at 2:29am.

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

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