由 A^2 = E,B^2 = E
得 |A| = ±1,|B| = ±1.
再由 |A|+|B| = 0
得 |A||B| = -1.
所以有
-|A+B| = |A||A+B||B| = |A^2B + AB^2| = |B+A| = |A+B|
所以 |A+B| = 0.