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A real orthogonal matrix $A$ is proper if $\det A=1 $.

Find $2\times 2$ proper matrix $A$

I tried to use the fact that product of $A$ and its transpose is equal to identity.

But, there were bunch of equations which seem not related to each other and can not find such $A$.

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    $\begingroup$ Example: $2\times 2$ identity. $\endgroup$ – vadim123 Nov 6 '14 at 22:48
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For any $\theta$, $$ \begin{pmatrix} \cos\theta & \sin\theta\\ -\sin\theta & \cos\theta \end{pmatrix} $$ is such a matrix. Actually, they all have this form.

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  • $\begingroup$ Can u swap sin and cos? $\endgroup$ – Kein Nov 6 '14 at 23:05
  • $\begingroup$ try for instance to substract $\pi / 2$ to $\theta$. $\endgroup$ – mookid Nov 6 '14 at 23:09

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