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?

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

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