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## Homework Statement

Suppose that A is a real n by n matrix which is orthogonal, symmetric, and positive definite. Prove that A is the identity matrix.

## Homework Equations

Orthogonality means [itex]A^t=A^{-1}[/itex], symmetry means [itex]A^t=A[/itex], and positive definiteness means [itex]x^tAx>0[/itex] whenever x is a nonzero vector.

## The Attempt at a Solution

Messing around with inner products, trying to show that the matrix [itex]A-I[/itex] is the zero matrix. Help is appreciated.