# Upper and Lower Triangular Matrix

Let be $$\alpha∈R, n≥2$$, and let be $$A∈\textbf{X}_\textbf{n}\textbf{(R)}$$ be a matrix satisfying the equation $$A^n+\frac{1}{4} α^2 A^{(n-2)}=αA^{(n-1)}$$ Prove that $$A$$ is similar to an upper triangular matrix and lower triangular matrix.

Thank you.

• Please try formatting your question with TeX as in math.stackexchange.com/help/notation it will make it far more readable. – Alex J Best May 3 at 10:07
• I would start by factorising and after cancelling the A to n-2 you can solve as a quadratic – W M Seath May 3 at 10:12