1. The problem statement, all variables and given/known data Suppose that A is an n x n matrix such that A(Transpose)A=I. Let x be any vector in R^n. Show that llAxll=llxll; that is, multiplication of x by A produces a vector Ax having the same length as x. 2. Relevant equations Sqrt(x(transpose)x)=llxll 3. The attempt at a solution So I started setting up the equation wth an n x n matrix... l a b l =A l c d l l a c l= A (transpose) l b d l A(transpose)A= I= l a^(2) +c^(2) ab+cd l l ba+dc b^(2)+d^(2)l then I let the vector x= l x1 l l x2 l then from there I was going to use the distance formula on Ax but I wasn't sure if doing the dot product of Ax is the same thing as matrix multiplication of Ax, and my second problem is that I am not sure how to take the square root of a 2x2 matrix if they are the same thing. If someone can answer those to questions for me I think I can finish the problem. Thank you.