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

[mcbonov]

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.

 

[tiny-tim]

welcome to pf!

hi mcbonov! welcome to pf!

(try using the X² icon just above the Reply box )

… use the properties of the determinant.

the determinant of the product is the product of the determinants