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Linear Algebra

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Orthogonal Matrices

LINALG-EX3KXK

Which of the following matrices is orthogonal?

A

$\begin{pmatrix} 1 & 0 & 0 \\\ 0 & 2 & 0 \\\ 0 & 0 & 3 \end{pmatrix} $

B

$\begin{pmatrix} 1 & 1 & -1 \\\ -1 & 1 & 1 \\\ 1 & -1 & 1 \end{pmatrix}$

C

$ \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 0 & 0 \end{pmatrix}$

D

$\begin{pmatrix} 1/\sqrt{2} & 1/\sqrt{3} & 0 \\\ -1/\sqrt{2} & 1/\sqrt{3} & 1/\sqrt{2} \\\ 0 & 1/\sqrt{3} & 1/\sqrt{2} \end{pmatrix}$

E

$\begin{pmatrix} 1 & 1 & 1 \\\ 1 & 1 & 1 \\\ 1 & 1 & 1 \end{pmatrix}$