Originally Posted by

**jedoob** Thanks. I understand this, but what I don't understand is as follows:

I have two different 3x3 matrices infront of me, they both reduce to become the identity matrix . . .

BUT for some reason-the characteristic polynomial for one of them is (X-1)^3as expected but I know that this isn't true for the other one.

Please could you explain why this should be so and also how I could find: det(LI-A) for a 3x3 matrix A directly, instead of reducing it to rref and then finding the determinent.

[NOTE: I would also need to find the minimum polynomial afterwards so pref I need a method which will give me the det factorised as much as possible.]