- #1
soothsayer
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Homework Statement
Show that a product of orthogonal matrices is orthogonal.
Homework Equations
Orthoganol matrix: M-1=MT
The Attempt at a Solution
since A-1=AT
A-1 and AT commute.
commutable => symmetric => A-1AT=(A-1AT)T
(A-1AT)-1=A-1AT/det(A-1AT)
=> (A-1AT)-1(A-1AT)=(A-1AT)2/det(A-1AT)
M-1M=I
M2=-I
=> I=-I/det(A-1AT)=> det(A-1AT) = -1
=> (A-1AT)-1=-(A-1AT)
=> (A-1AT)-1=/=A-1AT ??
I'm sure I did something wrong here. Probably overstepped an assumption. Can anyone help?