Suppose $AB = BA$ and $A^2+B^2 = I$, where A and B are complex matrices.
My feeling is that this implies that both A and B are diagonal matrices. But I'm having trouble proving it.
Appreciate any help.
Suppose $AB = BA$ and $A^2+B^2 = I$, where A and B are complex matrices.
My feeling is that this implies that both A and B are diagonal matrices. But I'm having trouble proving it.
Appreciate any help.
Consider the matrices $A=\binom{0\ 0}{0\ 0}$ and $B=\binom{0\ 1}{1\ 0}$.