P and Q are two 2x2 matrices and I is a 2x2 unit matrix.

Is it ever the case that PQ - QP = I?

(In reply to Solution and a variant by Jer)

PQ+QP=-I => bg+cf=1, f(a+d)+b(h+e)=0, c(h+e)+g(a+d)=0

So take g=(1-cf)/b, h=-e, d=0-a -- any matrices of that form will work, but other forms exist as well.

Posted by Gamer on 2007-04-11 19:25:43