If the matrix $\left(\begin{array}{ccc}0 & a & a \\ 2 b & b & -b \\ c & -c & c\end{array}\right)$ is orthogonal, then the values of $a, b, c$ are

Let $A=\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5\end{array}\right]$. If $|A|^2=25$, then $|\alpha|$ equals to

An $n \times n$ matrix is formed using 0, 1 and $-$1 as its elements. The number of such matrices which are skew symmetric is

Suppose $\alpha, \beta, \gamma$ are the roots of the equation $x^3+q x+r=0($ with $r \neq 0)$ and they are in A.P. Then the rank of the matrix $\left(\begin{array}{lll}\alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta\end{array}\right)$ is