A scalar matrix is a square matrix of the form I (I the identity matrix), for some scalar ; i.e. a scalar matrix is a

A scalar matrix is a square matrix of the form λI (I the identity matrix), for some scalar λ; i.e. a scalar matrix is a diagonal matrix in which all diagonal entries are equal
a) Prove that if a square matrix A is similar to a scalar matrixλI, then A=λI.
b) Prove that a diagonalizable matrix with just one eigenvalue is a scalar matrix.
c) Show that is not diagonalizable.

1 1