query: if $A\times B = A$, is $B ={} $Identity matrix?
positive_passages.docid: 147490
positive_passages.text: If matrix $AB=A$, does it mean B must be an identity matrix?
negative_passages.docid: 39455
negative_passages.text: Prove that $(X\times Y)\setminus (A\times B)$ is connected
negative_passages.docid: 48658
negative_passages.text: Let $A$ and $B$ be $n\times n$ matrices. Suppose $A$ is similar to $B$. Prove trace($A$) = trace($B$).
negative_passages.docid: 55062
negative_passages.text: $2\times 2$ matrix $C=AB-BA$
negative_passages.docid: 109312
negative_passages.text: How is the matrix identity $\det\begin{pmatrix}A&B\\B&A\end{pmatrix}=\det(A+B)\det(A-B)$ proved?
negative_passages.docid: 145719
negative_passages.text: Similarity between $A$ and $B (2\times 2)$.
negative_passages.docid: 147903
negative_passages.text: Similar matrices-Identity
negative_passages.docid: 73697
negative_passages.text: Let $A, B$ be $n\times n$ with $n\ge 2$ nonsingular matrices with real entries such that $A^{-1} + B^{-1} =(A+B)^{-1}$
negative_passages.docid: 38200
negative_passages.text: Show that $(\mathbf{a}·\mathbf{a})(\mathbf{b}·\mathbf{b})-(\mathbf{a}·\mathbf{b})^2=(\mathbf{a}\times\mathbf{b})·(\mathbf{a}\times\mathbf{b})$?
negative_passages.docid: 3301
negative_passages.text: If $AB = I$ then $BA = I$
negative_passages.docid: 76823
negative_passages.text: Is it the case that for all sets $A, B, C,$ and $D$, $(A \times B) \cup (C \times D) = (A \cup B) \times (C \cup D)$?
negative_passages.docid: 123044
negative_passages.text: Commutative matrices are multiples of the identity
negative_passages.docid: 83475
negative_passages.text: Prove Or Disprove: tr(AB)=tr(A)*tr(B)
negative_passages.docid: 44100
negative_passages.text: Prove that identity element is unique
negative_passages.docid: 63267
negative_passages.text: Under what conditions on the sets $A$ and $B$ will it be true that $A\times B= B\times A$
negative_passages.docid: 46875
negative_passages.text: The identity morphism in $\mathbf{Set}$ is the identity function
negative_passages.docid: 106305
negative_passages.text: Prove/disprove: if $\det(A+X) = \det(B + X)$ for all $X$, then $A=B$