# Matrix determinant inequality

Knowing that $$A$$ and $$B$$ are $$2$$ matrices of $$2\times2$$ with elements on $$\mathbb{R}$$, we have to prove that $$\det(A^2+B^2)\ge\det(AB-BA)$$ I tried calculating it directly and got nothing. Any ideas?

• Thanks for the edit. I'm pretty much new to this site and also quite tired right now. – Wolfuryo Nov 28 '18 at 20:34
• Answered in the answer provided by user1551 in math.stackexchange.com/questions/756373/… – NoChance Nov 28 '18 at 21:19