A scalar matrix is a square matrix of the form $\displaystyle \lambda\$for some scalar $\displaystyle \lambda\$ that is, a scalar matrix is a diagonal matrix in which all the entries are equal.I

a) Prove that if a square matrix A is similar to a scalar matrix $\displaystyle \lambda\$Then A=$\displaystyle \lambda\$I,Show that a diagonalizable matrix having only one eigenvalue is a scalar matrix.I

b)

c) Prove that $\displaystyle \begin{pmatrix}\ 1 & 1 \\ 0 & 1 \end{pmatrix}\$ is not diagonalizable.