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Theoretical diagonalazation question

there is
[tex]
A\epsilon M_{2x2}(Q)
[/tex]
I am given that A is diagonazable
prove that
A)
[tex]
A^10+12A
[/tex]
is diagonizable too

B)give an example for a matrix B\epsilon M_{2x2}(Q)
that is not diagonizable,but b^2 is diagonisable
??

i know that the eigenvalues of a matrix are the same as for every matrix
like A^10 or A^3+2A+3I etc..

but i dont now how to show what they ask
??
 
Last edited:
i mistakeny put it here
it should be on calculus
 

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