Show that if for a square matrix $A$ satisfies $A^3+ 4A^2 - 2A + 7I = 0 $ then so does $A^T$

I suspect that this is not always true so I need to do an example not the general case ( I partially suspect this cause the next question asks me if this is always true or sometimes false so I need to find a counter-example as well)

not really sure where to start this problem.