query: Proof: if $AB=BA$, prove that $(AB)^2 = A^2B^2$
positive_passages.docid: 17032
positive_passages.text: If $ab=ba$, Prove $a^2$ commutes with $b^2$
negative_passages.docid: 146795
negative_passages.text: Proof If $AB-I$ Invertible then $BA-I$ invertible.
negative_passages.docid: 74222
negative_passages.text: If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
negative_passages.docid: 12927
negative_passages.text: $A^2+B^2=AB$ and $BA-AB$ is non-singular
negative_passages.docid: 55062
negative_passages.text: $2\times 2$ matrix $C=AB-BA$
negative_passages.docid: 110944
negative_passages.text: Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
negative_passages.docid: 31783
negative_passages.text: Is this proof of $ab = 0$ correct?
negative_passages.docid: 90486
negative_passages.text: If $(A-B)^2=O_2$ then $\det(A^2 - B^2)=(\det(A) - \det(B))^2$
negative_passages.docid: 128760
negative_passages.text: If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?
negative_passages.docid: 136304
negative_passages.text: Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
negative_passages.docid: 63535
negative_passages.text: Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
negative_passages.docid: 136868
negative_passages.text: Prove that $\sqrt{a^2+3b^2}+\sqrt{b^2+3c^2}+\sqrt{c^2+3a^2}\geq6$ if $(a+b+c)^2(a^2+b^2+c^2)=27$
negative_passages.docid: 102742
negative_passages.text: order $a$ = 5, $a^3b = ba^3$. show that that $ab = ba$.
negative_passages.docid: 15191
negative_passages.text: If $a^2$ divides $b^2$, then $a$ divides $b$
negative_passages.docid: 47949
negative_passages.text: If $a$ and $b$ are two roots of $x^4 + x^3 - 1 = 0$ prove that $ab$ is a root of $x^6 + x^4 + x^3 - x^2 - 1$.
negative_passages.docid: 23080
negative_passages.text: Prove that $a^2(b+c-a)+b^2(a+c-b)+c^2(a+b-c) \leq 3abc.$
negative_passages.docid: 45760
negative_passages.text: if G is generated by {a,b} and ab=ba, then prove G is Abelian