1. Problematic Inverses

Hey Math Help Forum Community,

I need your help. I cannot solve these problem involving matrices and was hoping you could help me.

In the first problem I get a polynomial to the third degree with k which has to equal to zero. But I only get one root, not 3. Can anyone get the roots for me?

I can't do the second one at all, but I suspect -2 makes the rank = 2.

If you are going ask someone to find the roots for you, you could at least supply the cubic polynomial! When you say you got only one root, do you mean it was a triple root? That is, that the polynomial reduced to $(k- a)^3= 0$ for your solution, a? I don't get that. It is fairly easy to row-reduce to a triangular matrix and then the determinant is just the product of the numbers on the main diagonal- and here, those are just linear terms in k!