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

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SUMMARY

If U is an orthogonal matrix, then its determinant is either 1 or -1. This conclusion is derived from the property that the transpose of U, denoted as U^t, is equal to its inverse, U^-1. Since U is invertible, its determinant is non-zero, and by applying the property that the determinant of the product of matrices equals the product of their determinants, it follows that det(U) must equal ±1.

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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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welcome to pf!

hi mcbonov! welcome to pf! :smile:

(try using the X2 icon just above the Reply box :wink:)
mcbonov said:
… use the properties of the determinant.

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

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