query: Prove that $MN-NM$ is singular.
positive_passages.docid: 12927
positive_passages.text: $A^2+B^2=AB$ and $BA-AB$ is non-singular
negative_passages.docid: 62111
negative_passages.text: Functional Equation $f(mn)=f(m)f(n)$.
negative_passages.docid: 109573
negative_passages.text: Is sum of two orthogonal matrices singular?
negative_passages.docid: 81181
negative_passages.text: Prove that $\det(M-I)=0$ if $\det(M)=1$ and $MM^T=I$
negative_passages.docid: 14581
negative_passages.text: How do we prove $n^n \mid m^m \Rightarrow n \mid m$?
negative_passages.docid: 120065
negative_passages.text: Niven’s theorem proof.
negative_passages.docid: 68449
negative_passages.text: $\operatorname{Supp}(M)=V(\operatorname{Ann}M)$ if $M$ is finitely generated
negative_passages.docid: 144745
negative_passages.text: Proof of: If $x_0\in \mathbb R^n$ is a point of local minimum of $f$, then $\nabla f(x_0) = 0$.
negative_passages.docid: 65162
negative_passages.text: Show that $\dim H^0(\mathbb{P}^n, \mathcal{O}_{\mathbb{P}^n}(m)) = {n + m \choose n}$ if $m \geq 0$, and $0$ otherwise.
negative_passages.docid: 49294
negative_passages.text: prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$
negative_passages.docid: 28108
negative_passages.text: Proving the kernel is a normal subgroup.
negative_passages.docid: 147888
negative_passages.text: Show that $M=\bigcap_{\mathfrak{p}\in\operatorname{Spec}(R)}M_\mathfrak{p}=\bigcap_{\mathfrak{m}\in\text{Max}(R)}M_\mathfrak{m}$ for certain $M$.
negative_passages.docid: 34520
negative_passages.text: Is $0\,\mathrm{m}$ dimensionless?
negative_passages.docid: 55272
negative_passages.text: Prove that all nxn nilpotent matrices of order n are similar.
negative_passages.docid: 152932
negative_passages.text: Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
negative_passages.docid: 20504
negative_passages.text: $\forall m,n \in \Bbb N$ : $\ 56786730\mid mn(m^{60}-n^{60})$
negative_passages.docid: 27629
negative_passages.text: How to prove that $S^{2n+1}/S^1$ is homeomorphic to $\mathbb CP^n$ under a given identification