Answer to Question #2665 in Linear Algebra for nafeh
2 -2 1
1 2 2)
Prove that A is the product of a rotation and a reflection. Prove that A is an orthogonal matrix.
& a) the sum of squares of any row of A is equal to 1:
e.g. for the first row:
b) the scalar product of any two distinct rows is zero, e.g for the first and second rows:
1) Prove A is the product of a rotation and a reflection.
Due to 2) we know that A is orthogonal. If det(A)>0, then A is a rotation,& while for det(A)<0 it is a of a product of rotation and a reflection.
Thus it is necessary to show that det(A)<0.
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