Exercise: An Application to Markov chains

[sshh]

If A 2x2, show that A^-1 = A^T if and only if :
http://www.mathhelpforum.com/math-help/attachments/f5/20406d1294835445-exercise-application-markov-chains-untitled.png

[Hint: If a^2+b^2=1, then a=cosθ, b= sinθ for some θ. Use cos(θ-)=cosθcosϕ+sinθsinϕ]

 

[Mark44]

If A 2x2, show that A^-1 = A^T if and only if :
http://www.mathhelpforum.com/math-help/attachments/f5/20406d1294835445-exercise-application-markov-chains-untitled.png

[Hint: If a^2+b^2=1, then a=cosθ, b= sinθ for some θ. Use cos(θ-)=cosθcosϕ+sinθsinϕ]

Welcome to Physics Forums!
As a new member, you probably don't realize that you need to show some effort at solving your problem before we can give you any help. That's covered in the Rules, which you can see by clicking the Rules button in the menu across the top of the page.

There is a term missing in your hint. It should read. "Use cos(θ-ϕ)=cosθcosϕ+sinθsinϕ]"