query: Prove that $AB-BA=I_2$ cannot hold whatever the real $2\times 2$ matries $A, B$
positive_passages.docid: 7622
positive_passages.text: $AB-BA=I$ having no solutions
negative_passages.docid: 12927
negative_passages.text: $A^2+B^2=AB$ and $BA-AB$ is non-singular
negative_passages.docid: 72313
negative_passages.text: Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$
negative_passages.docid: 15626
negative_passages.text: Relations of a~b iff b = ak^2
negative_passages.docid: 25870
negative_passages.text: Prove that $0 \leq ab + ac + bc - abc \leq 2.$
negative_passages.docid: 26570
negative_passages.text: Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
negative_passages.docid: 123555
negative_passages.text: Proving that if $ab=e$ then $ba=e$
negative_passages.docid: 125668
negative_passages.text: A proof that BS(1,2) is not polycyclic
negative_passages.docid: 64077
negative_passages.text: $I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
negative_passages.docid: 115460
negative_passages.text: Proving $a\mid b^2,\,b^2\mid a^3,\,a^3\mid b^4,\ldots\implies a=b$ - why is my approach incorrect
negative_passages.docid: 66709
negative_passages.text: Are the matrix products $AB$ and $BA$ similar?
negative_passages.docid: 142980
negative_passages.text: If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
negative_passages.docid: 145980
negative_passages.text: For every matrix $A\in M_{2}( \mathbb{C}) $ there's  $X\in M_{2}( \mathbb{C})$ such that $X^2=A$?
negative_passages.docid: 62474
negative_passages.text: If $AB=I_n$ and $BA=I_m$ then $n=m$.
negative_passages.docid: 129743
negative_passages.text: $A$ be a $2\times 2$ real matrix with trace $2$ and determinant $-3$
negative_passages.docid: 109745
negative_passages.text: If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
negative_passages.docid: 68014
negative_passages.text: Prove that $\mathfrak{su}(2)$ is not isomorphic to $\mathfrak{sl}(2,\mathbb R)$