MathDB

Let

v \in \mathbb{R}^2

a vector of length 1 and

A

2 \times 2

matrix with real entries such that: (i) The vectors

A v, A^2 v

A^3 v

are also of length 1. (ii) The vector

A^2 v

isn't equal to

\pm v

nor to

\pm A v

. Prove that

A^t A=I_2

Problem Statement