If U is an orthogonal matrix,its determinant is equal to 1 or -1.

mcbonov
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Question:
Prove that is U is an orthogonal matrix, then the determinant of U is equal to 1 or -1.
Hint consider the equation U^t = U^-1 and use the properties of the determinant.


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So far I only found out ,since it is invertible ,its determinant is not zero.
I can't go any further than that...
Please help me.
 
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hi mcbonov! welcome to pf! :smile:

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mcbonov said:
… use the properties of the determinant.

the determinant of the product is the product of the determinants :wink:
 

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