234 5. Further Determinant Theory
It follows that there exist at least two solutions of the equation|X+Y|=|X|+|Y|,n=2,namely
X=PQ+QP or P2
−Q2
,Y=PQ−QP.
Furthermore, the equation
|X−Y+Z|=|X|−|Y|+|Z|,n=2,is satisfied by
X=P
2
−Q2
,Y=PQ+QP,
Z=2PQ.
Are there any other determinantal identities of a similar nature?