Yo !

I've a problem about kernel and endomorphism. And i'm a little bit worried 'cause i'm blocked when i've just answered the first question. But let's see...

Ok, so we have a -vector space and an endomophism of .

We have and .

So, i've prooved that we always have, for all ,

and

Now, the question is

Ok, now of course i've searche for a little while. But the fact is : i can't see how to start the proof. I think of several way : to prove it directly, maybe by induction, i've even think of trying it with contraposition !Show that, if , then

Well, so i really don't want the answer ! Please !

But just thesmallest hint( such as, the way to prove it ) which can make me see how to keep going.

Thanks for reading me ! And i apologize if my english is poor

Hugal.