$\displaystyle A=\begin{vmatrix}

1 & 0&0 \\

3& \omega &0\\

0&3-i&\omega^2

\end{vmatrix}\\$

where i is iota and w is cube root of unity.

Find

1) $\displaystyle A^{105}$

2) $\displaystyle A^{106}$

3) $\displaystyle A^{108}$

4) $\displaystyle A^{109}$