Is it possible to prove that $\text{tr}(AB)=\text{tr}(BA)$ without using matrices?
90475
Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
130498
Linear algebra proof regarding matrices
106986
Eigenvalues of $AB$ and $BA$
6091
Similarity of products $AB$ and $BA$ of square matrices
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
33448
Proof if $AB+BA=0$ Then atleast one of the matrices are singular.
125763
If $\mathrm{tr}(A)=0$, then we have $A=BC-CB?$
73155
Prove that for any square matrix, an invertible matrix B exists, so that BA is triangular
130253
Differentiating $\mbox{tr} (ABA^TC)$ w.r.t. $A$
155884
What are the conditions on $\text{tr}(AB) \leq \text{tr(A)} \text{tr(B)}$ to be true?
141173
Are there matrices such that $AB=I$ and $BA \neq I$
140290
Solving $AB - BA = C$
99585
Do the non-zero eigenvalues of AB and BA have the same algebraic multiplicity (for AB and BA not square)?
74460
Matrices A+B=AB implies A commutes with B
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?
55031
Show any matrix $A_{n\times n}$ can be written as sum of two nonsingular matrices
80544
Need verification - Prove a Hermitian matrix $(\textbf{A}^\ast = \textbf{A})$ has only real eigenvalues