Recent content by mcbonov

i tried Ax =λx (Ax-λx)=0 (A-λ)x=0 since x is not a zero vector A-λ=0 then A=λ THEN A^-1 = λ^-1 so (A^-1)x = (λ^-1)x I basically don't know how to prove... I don't think the above is near to correct answer. that's the most I can do ... how can i solve this problem??

Homework Statement Let A be an invertible matrix. show that if λ is an eigenvalue of A, then 1/λ is an eigenvalue of A^-1 PLEASE HELP ME . Thank you.

Question: Prove that is U is an orthogonal matrix, then the determinant of U is equal to 1 or -1. Hint consider the equation U^t = U^-1 and use the properties of the determinant. ------------------------------------------------------------------------------------------- So far I only...