Question: Let A = I avv^T where v is a nonzero vector in R^n, I is the (n n) identity matrix and a is the scalar

Let A = I avv^T where v is a nonzero vector in R^n, I is the (n n) identity matrix and a is the scalar given by a = 2 / (v^T * v) Show that A is symmetric and that AA = I; that is A^1 = A

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