If $A = \begin{bmatrix} a & b \\ c & -a \end{bmatrix}$ is such that $A^2 = I$,then . . . . . . .

The characteristic roots of the matrix $\left[\begin{array}{ccc}1 & 0 & 0 \\ 2 & 3 & 0 \\ 4 & 5 & 6\end{array}\right]$ are

Let $T$ and $U$ be the set of all orthogonal matrices of order $3$ over $\mathbb{R}$ and the set of all non-singular matrices of order $3$ over $\mathbb{R}$ respectively. Let $A = \{-1, 0, 1\}$. Then:

If $A = \begin{bmatrix} a & b \\ b & a \end{bmatrix}$ and $A^2 = \begin{bmatrix} \alpha & \beta \\ \beta & \alpha \end{bmatrix}$,then:

If for $A = \begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}$,$A^2 = I$,then . . . . . . .

If $A = \begin{bmatrix} \cos \frac{2 \pi}{33} & \sin \frac{2 \pi}{33} \\ -\sin \frac{2 \pi}{33} & \cos \frac{2 \pi}{33} \end{bmatrix}$,then $A^{2017} = $