a) Unitary matrices are normal matrix hence diagonalizable as a consequence of spectral theorem
b)same as a)
c)No idea.but I think it may not be diagonalizable unless it has one eigen value with dimension of eigen space $1$
d) No idea.
a) Unitary matrices are normal matrix hence diagonalizable as a consequence of spectral theorem
b)same as a)
c)No idea.but I think it may not be diagonalizable unless it has one eigen value with dimension of eigen space $1$
d) No idea.
Hint: The shear matrix $\left[\begin{array}{cc} 1 & 1\\ 0 & 1 \end{array}\right]$ has two real eigenvalues (both equal $1$) complex entries, and cannot be diagonalized.