Computing a Proof Regarding Eigenvectors and Matrices

D and E are nxn matrices, E is invertible, DE = ED, and u is an eigenvector for D corresponding to x=5.

a. Show that Eu is also an eigenvector for D corresponding to x=5.

b. Show that u is an eigenvector for D^2.

c. Show that u is an eigenvector for
D^2 - 3D.

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...*) which can be rewritten as D(Eu)=5(Eu) so indeed Eu is an eigenvector corresponding to the eigenvalue x=5.

b) To get D62 we multiply again the equality Du=5u by D to the left. ...