query: Prove there exist $2 \times 2$ matrix $B$ such that $B^3=A^2$, for every $A$.
positive_passages.docid: 152102
positive_passages.text: Prove that for every complex $2$x$2$ matrix $A$, there exists a matrix $X$ such that $X^3=A^2$.
negative_passages.docid: 145980
negative_passages.text: For every matrix $A\in M_{2}( \mathbb{C}) $ there's  $X\in M_{2}( \mathbb{C})$ such that $X^2=A$?
negative_passages.docid: 12927
negative_passages.text: $A^2+B^2=AB$ and $BA-AB$ is non-singular
negative_passages.docid: 110256
negative_passages.text: Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
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: 20110
negative_passages.text: How to prove $(AB)^T=B^T A^T$
negative_passages.docid: 35757
negative_passages.text: A 2x2 matrix $M$ exists. Suppose $M^3=0$ show that (I want proof) $M^2=0$
negative_passages.docid: 23638
negative_passages.text: $a^2b^2+a^2c^2+b^2c^2\leq 3$
negative_passages.docid: 128990
negative_passages.text: Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
negative_passages.docid: 113907
negative_passages.text: All nilpotent $2\times 2$ matrices
negative_passages.docid: 64656
negative_passages.text: how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
negative_passages.docid: 11857
negative_passages.text: $A$ be a complex $3\times 3$ matrix such that $A^3=-I$
negative_passages.docid: 130498
negative_passages.text: Linear algebra proof regarding matrices
negative_passages.docid: 24809
negative_passages.text: For all square matrices $A$ and $B$ of the same size, it is true that $(A+B)^2 = A^2 + 2AB + B^2$?
negative_passages.docid: 158845
negative_passages.text: Given $A$ and $B$ positive-definite matrices and $Q$ unitary matrix, prove that if $A = BQ$, then $A=B$.
negative_passages.docid: 130327
negative_passages.text: Prove that $a^2 > b^2$ ; if $a > b \geq 0$.
negative_passages.docid: 52930
negative_passages.text: Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$