Let $A=\left[\begin{array}{ccc}\cos heta & 0 & -\sin heta \ 0 & 1 & 0 \ \sin heta & 0 & \cos heta\end{array} ight]$. If for some $ heta \in(0, \pi), A^2=A^T$, then the sum of the diagonal elements of the matrix $(\mathrm{A}+\mathrm{I})^3+(\mathrm{A}-\mathrm{I})^3-6 \mathrm{~A}$ is equal to _________ .

Question

Let $A=\left[\begin{array}{ccc}\cos 	heta & 0 & -\sin 	heta \ 0 & 1 & 0 \ \sin 	heta & 0 & \cos 	heta\end{array}ight]$. If for some $	heta \in(0, \pi), A^2=A^T$, then the sum of the diagonal elements of the matrix $(\mathrm{A}+\mathrm{I})^3+(\mathrm{A}-\mathrm{I})^3-6 \mathrm{~A}$ is equal to _________ .

Accepted Answer

Correct answer: 6

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