for 1.9 $trace(A)=1+w+w^2=0$, $A$ is not diagonalizable over reals as it has no three distinct real eigen values, $\lambda=1$ is an eigen value that is true.
for 1.10, a) let $\lambda$ be an eigen value, $Ax=\lambda x$ so $x^TAx=x^T\lambda x\ge 0$ so $\lambda\ge 0$ so a) is true, b) is false if some $\lambda=0$ then $A$ is surely not invertible as detA=product of eigen values. c) i have no idea please help.