Determine if the matrix is orthogonal
$\displaystyle \left(\begin{array}{ccc}0&0&1\\1&0&0\\0&1&0\end{ar ray}\right)
$
I don't know how to do it. Any help is appreciated! Thanks!
I'm not sure what that means or how to figure it out...
But here is the whole question: Consider the unit cube in $\displaystyle \Re^3 $ based at the origin in the (+,+,+) octant. Let $\displaystyle \theta $ be an angle. Determine if the matrix is orthogonal.
$\displaystyle A = \left(\begin{array}{ccc}0&0&1\\1&0&0\\0&1&0\end{ar ray}\right) $
$\displaystyle A^{T} = \left(\begin{array}{ccc}0&1&0\\0&0&1\\1&0&0\end{ar ray}\right) $
$\displaystyle AA^{T} = A^{T}A = \left(\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{ar ray}\right) = I$
so A is orthogonal