Let A=(2−131)A = \begin{pmatrix} 2 & -1 \\ 3 & 1 \end{pmatrix}A=(23−11) and B=(021−1)B = \begin{pmatrix} 0 & 2 \\ 1 & -1 \end{pmatrix}B=(012−1). Which of the following statements are true?
AB=BAAB = BAAB=BA
AB≠BAAB \neq BAAB=BA
det(AB)=det(BA)\text{det}(AB) = \text{det}(BA)det(AB)=det(BA)
tr(AB)=tr(BA)\text{tr}(AB) = \text{tr}(BA)tr(AB)=tr(BA) (trace is the sum of diagonal entries)