Eigen vector & Eigen Value

Hi: I am struggling with this question.

Given a vector R->SO(3) R=[r11 r12 r13;r21 r22 r23;r31 r32 r33] How can we show that e=[r32-r23 r13-r31 r21-r12]'('=transpose) is an eigen vector of R with unity eigen value? Any suggestion/ideas will be appreciated.

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Neil
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