query: Proof if $AB = BA$ is not verified, then $AB$ is not symmetric.
positive_passages.docid: 18800
positive_passages.text: If A and B are symmetric is AB=BA true?
negative_passages.docid: 62474
negative_passages.text: If $AB=I_n$ and $BA=I_m$ then $n=m$.
negative_passages.docid: 139841
negative_passages.text: Proving $A\setminus(B\setminus C)$ is not equal to $(A\setminus B)\setminus C$
negative_passages.docid: 6096
negative_passages.text: If $A+B=AB$ then $AB=BA$
negative_passages.docid: 61538
negative_passages.text: Given a square matrix $A$, both $AA^T$ and $A^TA$ are symmetric
negative_passages.docid: 104124
negative_passages.text: Prove or disprove: $A-(B-C) = (A-B)-C$
negative_passages.docid: 7622
negative_passages.text: $AB-BA=I$ having no solutions
negative_passages.docid: 99585
negative_passages.text: Do the non-zero eigenvalues of AB and BA have the same algebraic multiplicity (for AB and BA not square)?
negative_passages.docid: 109745
negative_passages.text: If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
negative_passages.docid: 105921
negative_passages.text: Why do we have $ab=ba$?
negative_passages.docid: 6091
negative_passages.text: Similarity of products $AB$ and $BA$ of square matrices
negative_passages.docid: 70021
negative_passages.text: Verify if symmetric matrices form a subspace
negative_passages.docid: 102742
negative_passages.text: order $a$ = 5, $a^3b = ba^3$. show that that $ab = ba$.
negative_passages.docid: 145876
negative_passages.text: $AB-BA=A$ implies $A$ is singular and $A$ is nilpotent.
negative_passages.docid: 31783
negative_passages.text: Is this proof of $ab = 0$ correct?
negative_passages.docid: 20110
negative_passages.text: How to prove $(AB)^T=B^T A^T$
negative_passages.docid: 83475
negative_passages.text: Prove Or Disprove: tr(AB)=tr(A)*tr(B)