query: $AB = C$, prove if $C$ is invertible, then $A$ and $B$
positive_passages.docid: 25488
positive_passages.text: Let $A,B$ be $m\times m$ matrices such that $AB$ is invertible. Show $A,B$ invertible.
negative_passages.docid: 31783
negative_passages.text: Is this proof of $ab = 0$ correct?
negative_passages.docid: 147246
negative_passages.text: If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
negative_passages.docid: 17032
negative_passages.text: If $ab=ba$, Prove $a^2$ commutes with $b^2$
negative_passages.docid: 51321
negative_passages.text: Prove that $A = B = C = D$
negative_passages.docid: 151038
negative_passages.text: How to prove (A v B), (A → C), (B → D) therefore (C v D)
negative_passages.docid: 21726
negative_passages.text: Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
negative_passages.docid: 118981
negative_passages.text: Proving $\sqrt{ab} = \sqrt a\sqrt b$
negative_passages.docid: 7034
negative_passages.text: Prove that $A+I$ is invertible if $A$ is nilpotent
negative_passages.docid: 136854
negative_passages.text: Prove: For a,b,c positive integers, ac divides bc if and only if a divides b
negative_passages.docid: 111763
negative_passages.text: True or False $A - C = B - C $ if and only if $A \cup C = B \cup C$
negative_passages.docid: 3301
negative_passages.text: If $AB = I$ then $BA = I$
negative_passages.docid: 104068
negative_passages.text: Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$
negative_passages.docid: 50266
negative_passages.text: In the following figure prove that: $AK||BC$
negative_passages.docid: 145058
negative_passages.text: Prove $ (A \cup B) \cap C$ = $(A \cap C) \cup (B \cap C) $
negative_passages.docid: 90438
negative_passages.text: To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$
negative_passages.docid: 53113
negative_passages.text: $I-AB$ be invertible $\Leftrightarrow$ $I-BA$ is invertible