# Homework Help: Theoretical diagonalazation question

1. Mar 2, 2009

### 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 dont now how to show what they ask
??

Last edited: Mar 2, 2009
2. Mar 2, 2009

### transgalactic

i mistakeny put it here
it should be on calculus