P and Q are two 2x2 matrices and I is a 2x2 unit matrix.
Is it ever the case that PQ - QP = I?
Matricies formatted as best I could:
P = |c d|
Q = |e f|
PQ - QP = |(bg-cf) (af+bh-be-df)|
To equal I, (bg-cf) = 1 = (cf-bg) which is clearly impossible.
So it is never the case that PQ - QP = I
An error in my first attempt led to
P = |-2 1|
| 2 2|
Q = |1 1|
And PQ + QP = -I
Posted by Jer
on 2007-04-11 13:36:30