Which of the following matrices A is idempotent. Matrix I is an identity matrix, matrix M is any invertible matrix and vector b is any vector, all of compatible sizes. To answer the question create random matrices and vectors M, b etc, compute matrix A and verify that it is idempotent using the norm trick. Remember a matrix A is idempotent when it is equal to its square (A * A)

a.

A = eye(5) - (M*b*b*M)/trace(M*b*b*M)

b.

A = eye(5) - (M*b*b'*M')/trace(b*b')

c.

A = eye(5) - (M*b*b'*M')/trace(M*b*b'*M')

d.

A = eye(5) - (b*b')/trace(M*b*b'*M')

e.

A = eye(5) - (M*b*b'*M')