1. Let A be an n x n matrix in reduced row echelon form. If A is not equal to I

_{n}(identity matrix), prove that A has a row consisting entirely of zeros.

2. If A = [a b which is a 2 x 2 matrix;

c d]

show that A is nonsingular if and only if ad-bc is not equal to zero

- So far I know that if the determinant is not equal to zero, then the inverse of A exists. I am stuck on the next step..

3. Find all values of a for which the inverse of the matrix exists. What is A inverse?

A= (1 1 0 ; 3 x 3 matrix

1 0 0

1 2

**a**)

Thanks in advance