Theoretical diagonalazation question

[transgalactic]

there is
$$A\epsilon M_{2x2}(Q)$$
I am given that A is diagonazable
prove that
A)
$$A^10+12A$$
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 don't now how to show what they ask
??

 

[transgalactic]

i mistakeny put it here
it should be on calculus