We use the Cayley-Hamilton identity for
We have
and
Then
or
Another challenge problem, inspired by an earlier question.
Given arbitrary 2x2 matrices and , prove that
where is the trace of , is the trace of and is the trace of or of . is of course the 2x2 identity matrix.
Although a brute force approach would work, a more elegant solution would be welcome.
Enjoy.
Moderator approved. CB