Question: (Orthogonal Matrices) An orthogonal matrix is any square matrix B such that $$B'B = I$$. This means that $$B^{-1} = B'$$. A two-dimensional geometric example

(Orthogonal Matrices) An orthogonal matrix is any square matrix B such that $$B'B = I$$. This means that $$B^{-1} = B'$$. A two-dimensional geometric example of an orthogonal matrix as a transformation is one that rotates all vectors an equal amount around the origin. Another two-dimensional example is a reflection of all vectors in a line. Confirm these examples by showing that $$||x|| = ||Bx||$$ and

$$x'y = (Bx)'(By)$$ and interpreting these facts appropriately.

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