Seien ${\displaystyle {}a,b,c,d}$ reelle Zahlen mit

${\displaystyle {}a^{2}+b^{2}+c^{2}+d^{2}=1\,.}$

Zeige, das die Determinante der Matrix

${\displaystyle {\begin{pmatrix}a^{2}+b^{2}-c^{2}-d^{2}&2(-ad+bc)&2(ac+bd)\\2(ad+bc)&a^{2}-b^{2}+c^{2}-d^{2}&2(-ab+cd)\\2(-ac+bd)&2(ab+cd)&a^{2}-b^{2}-c^{2}+d^{2}\end{pmatrix}}}$

${\displaystyle {}1}$