How to find a real orthogonal matrix?

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Find a real orthogonal matrix of order 3, other than ±I3, having all integer elements.

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Hint:

Try to swap the columns of the matrix that you are not allowed to use.

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You can come up with a lot: \begin{equation} \pmb{A} = \begin{bmatrix} k_1 & 0 & 0 \\ 0 & k_2 & 0 \\ 0 & 0 & k_3 \\ \end{bmatrix} \end{equation} where $k_i$ are integers. There's a lot you can come up with.