Trace of AB = Trace of BA
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
102935
Trace and determinant of composition of a left-multiplication and a right-multiplication on a space of matrices
31606
Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?
55062
$2\times 2$ matrix $C=AB-BA$
99585
Do the non-zero eigenvalues of AB and BA have the same algebraic multiplicity (for AB and BA not square)?
72092
If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
102742
order $a$ = 5, $a^3b = ba^3$. show that that $ab = ba$.
72507
Does $ab=1$ imply $ba=1$ in a ring?
47829
Prove that $\operatorname{trace}(A^TA) = 0\ \iff\ A = 0$.
13346
If $A=AB-BA$, is $A$ nilpotent?
23224
$\mbox{rank}(A)=1$ implies $\det(A+I)=\mbox{trace}(A)+1$
74460
Matrices A+B=AB implies A commutes with B
3301
If $AB = I$ then $BA = I$
37061
The order of $ab$ when $a,b$ commute
110502
$AB=BA$ with same eigenvector matrix
64432
Physical or geometric meaning of the trace of a matrix
143608
Show the Trace$(B)^{2} \leq$ nTrace$(B^{T}B)$