show that if λ is an eigenvalue of matrix a then, λ^2 is an eigenvalue of A^2?
hi! i have to prove the sentence stated above, but i am not sure how.. and it really seems simple :/
from what i know i think i need too use Ax= λx where x is an eigenvector associated with λ
and that (A- λ i)x=0 ....but how? thank you!
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AX=λX eqn 1
(A=the matrix,X= eigen Vector,λ=eigen value )
premultiply by A on both the sides
A*AX=A* λX
A^2 *X=λ AX
now AX=λX from eqn 1
so A^2*X=λ*λX
A^2*X=λ^2 *X
thus the eigen value of A^2 is λ^2