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

## Answer this Question

## Related Questions

- LINEAR ALGEBRA - How to prove or disprove (a)if A has a zeronentryonthe diagonal...
- math - If A^TA is an invertible matrix, prove that the column vectors of A are ...
- Algebra - Let A and B be n x n matrices, assume AB is invertible and show that ...
- College Math : Linear Algebra - Suppose A is a square matrix satisfying the ...
- Linear Algebra - Consider the linear transformation T: R^3->R^3 which acts by...
- Math - Let A, B, and 0 be 2x2 matrices. Assuming that A is invertible, find a ...
- MATHS----Matrix - For a given square matrix A the predicted values of matrix B ...
- Matrix - Let A be an invertible n x n matrix, and let B be an n x p matrix. ...
- math - I need help with this one... Thanks!!!! Prove the following statement: ...
- Algebra - Some functions that aren't invertible can be made invertible by ...

More Related Questions