Consider the following matrices:

A1 = 1 1

1 0 ,

A2 = 1 0

0 0 ,

A3 = 1 1

1 1 ,

A4 = 0 1

0 0 ,

A5 = 1 −1

1 0.

A1,A2,A3,A4,A5 are 2*2 matrix, sorry for the format, I don't know how to type the matrix in computer.

1.Compute eigenvalues of each matrix, repeated according to multiplicity

2.Which of the matrices are singular?

3.For each i, either show that Ai cannot be diagonalized, or give invertible P anddiagonal D such that Ai = (p)(D)(P^(-1))