Let A be the following matrix:([-2,-3,0],[-3,6,0],[0,0,-3])

a) Enter its characteristic equation below.

Note you must use pas the parameter instead of λ, and you must enter your answer as a equation, with the equals sign.

b) Enter the eigenvalues of the matrix, including any repetition. For example (16,16,24).

c) Find the eigenvectors, and then use Gram-Schmidt to find an orthonormal basis for each eigenvalue's eigenspace. Build an orthogonal matrix whose columns are these eigenvectors. Enter this matrix, as a list of row vectors.

d) Enter the diagonal matrix (P^T)AP for your matrix P.