Which of the following is/are correct?

If P is a  $3\times 3$ orthogonal matrix, and  $\alpha ,\beta ,\gamma$ are angles made by a straight line with X, Y, Z axes respectively and if  $A=\left[\begin{array}{ccc}{\sin }^2\alpha & \sin \alpha \sin \beta & \sin \alpha \sin \gamma \\ \sin \alpha \sin \beta & {\sin }^2\beta & \sin \beta \sin \gamma \\ \sin \alpha \sin \gamma & \sin \beta \sin \gamma & {\sin }^2\gamma \end{array}\right]$,  $Q=P^T$ AP, then  $P{Q}^6{P}^T$ =32A

If matrix $A={\left[a_{ij}\right]}_{3\times 3}$ and matrix $B={\left[b_{ij}\right]}_{3\times 3}$ where $a_{ij}+a_{ji}=0$ and $b_{ij}-b_{ji}=0\forall$  i and j then $\text{A}{}^{28}\text{B}^{11}$ is a singular matrix

If A is a  $n\times n$ matrix such that  $a_{ij}=(i^2+j^2-5ij)(j-i)\forall$  i, j then trace $\left(A\right)\ne 0$ 

If A is a  $n\times n$ matrix such that  $a_{ij}=(i^2+j^2-5ij)(j-i)\forall$ i, j  then trace  $\left(A\right)=0$