query: Find all $2 \times 2$ matrices $A$ such that $AB = BA$ for every $2 \times 2$ matrix $B$
positive_passages.docid: 87136
positive_passages.text: All matrices which commute with all $2\times 2$ matrices
negative_passages.docid: 104653
negative_passages.text: $A$ and $B$ are $3\times 3$ real matrices such that $\operatorname{rank}(AB)=1$, then $\operatorname{rank}(BA$) can not be which of the following?
negative_passages.docid: 100656
negative_passages.text: $2\times2$ matrix $A$ such that $A$ has one independent eigenvector while $A^{2}$ has two independent eigenvectors
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: 72092
negative_passages.text: If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
negative_passages.docid: 3330
negative_passages.text: Square matrices, ABA = A?
negative_passages.docid: 62614
negative_passages.text: How to get matrix $A$ from $A^\top A=B$ with given symmetric matrix $b$?
negative_passages.docid: 18800
negative_passages.text: If A and B are symmetric is AB=BA true?
negative_passages.docid: 133482
negative_passages.text: $AB-BA$ is a nilpotent matrix if it commutes with $A$
negative_passages.docid: 84871
negative_passages.text: Determining the dimension of span$\{AB-BA : A,B \in M_{n \times n}(\mathbb R) \}$
negative_passages.docid: 25357
negative_passages.text: Matrices $B$ that commute with every matrix commuting with $A$
negative_passages.docid: 112353
negative_passages.text: Prove that all 2x2 orthogonal matrices can be expressed as Rotation or Reflection
negative_passages.docid: 84422
negative_passages.text: $AB=BA$, $AC=CA$ we need to show $BC=CB$
negative_passages.docid: 94037
negative_passages.text: Solving the matrix equation $AP=PB$, where $A$ and $B$ are similar
negative_passages.docid: 113907
negative_passages.text: All nilpotent $2\times 2$ matrices
negative_passages.docid: 78224
negative_passages.text: Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$
negative_passages.docid: 141173
negative_passages.text: Are there matrices such that $AB=I$ and $BA \neq I$