# N x x determinant problem

1. Nov 3, 2015

### kockabogyo

1. Given $A,B\in Mat _n(\mathbb{R})$

2. Show that:
a) $\det (A^2 + A + E)\geq 0$
b) $\det (E+A+B+A^2+B^2)\geq 0$ ,
where $E$ is the unit matrix.

3. My attempt at a solution
$A^2 + A + E$=$(A + E)^2 -2A$

pleas give me tips to solve

Last edited by a moderator: Nov 3, 2015
2. Nov 3, 2015

### Staff: Mentor

Something went wrong with the linear term, and I would choose a different term to square.

You can consider the cases $det(A)=0$ and $det(A) \neq 0$ separately, that gives more freedom to manipulate A in one case.

3. Nov 3, 2015

### kockabogyo

Thanks, yes, sorry not - 2A only -A , but than?

4. Nov 3, 2015

### Staff: Mentor

I would choose a different term to square. A term that doesn't leave an A outside.

5. Nov 3, 2015

### kockabogyo

O Yeah!.. I think I found it.. Cayley Hamilton's context A2 - Tr(A)*A+det(A)*E = O