Consider the matrix

 

Find the Eigenvalues of the matrix A. 

Find two (linearly independent) eigenvectors for this matrix. 

Show that the two eigenvectors are perpendicular (by showing that their Inner product. r+ r = 0). 

Find a similarity transformation, C, that will diagonally the matrix A (form the matrix C by normalizing the two eigenvectors and then using one of the normalized eigenvectors as the first column and the second normalized eigenvector as the second column).

Show that the matrix C is Unitary.

A= (2 2 -1