Question: Linear Algebra question. I need Original solution . Thank you. (10 pts) Suppose U is a square matrix such that UU = 1,, and let

Linear Algebra question. I need Original solution. Thank you.

(10 pts) Suppose U is a square matrix such that U"U = 1,, and let x be any vector in R" (a) Show that (Ur) - (Ur) = 2 .I (Hint: convert the dot product version of the equation into the transpose version of the equation) (b) Show using part (a) that the only possible eigenvalues of U are 1 or -1

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