find eigen values of given matrix 
If $w$ is a non-real cube root of unity, then eigenvalues of the matrix:

$$ \begin{pmatrix} 1&1&1 \\ 1&w&w^2 \\ 1&w^2&w^4 \end{pmatrix}
   \begin{pmatrix} 1&0&0 \\ 0&-1&0 \\ 0&0&0 \end{pmatrix}
   \begin{pmatrix} 1&1&1 \\ 1&1/w&1/w^2 \\ 1&1/w^2&1/w^4 \end{pmatrix} $$

are which of these:

(a) $1,-1,0$
(b) $\frac{1}{3},-\frac{1}{3},0$
(c) $1,w,w^2$
(d) $3,-3,0$
Please suggest some trick to find eigen value of this matrix given as product of 3 matrices, because to actually compute product of these matrix would not be a feasible idea in a exam.

Hint: note that the matrix
$$
\frac 1{\sqrt{3}}\pmatrix{
1&1&1\\
1&\omega & \omega^2\\
1 & \omega^2 & \omega^4
}
$$
is unitary (since its columns are orthonormal). From there, it's easy to see that
$$
\left[
\frac 1{\sqrt{3}}\pmatrix{
1&1&1\\
1&\omega & \omega^2\\
1 & \omega^2 & \omega^4
}
\right]^{-1}=
\frac 1{\sqrt{3}}\pmatrix{
1&1&1\\
1&\omega^{-1} & \omega^{-2}\\
1 & \omega^{-2} & \omega^{-4}
}
$$
