Pauli Matrices form a Group

Theorem

Note that:

• $XY=-iZ$
• $YX=iZ$
• $YZ=-iX$
• $ZY=iX$
• $ZX=-iY$
• $XZ=iY$ Thus, $\{\pm X,\pm Y,\pm Z,I,\pm iX,\pm iY,\pm iZ,\pm iI\}$ forms a Group.