query: $A$ is an $n\times n$ matrix where $n$ is an even number. If $A^2 = 0$ what must also be true?
positive_passages.docid: 147014
positive_passages.text: Matrix algebra: If $A^2=0$, Proof rank(A) $\le \frac{n}{2}$
negative_passages.docid: 116539
negative_passages.text: Eigenvalues of matrix satisfying $A^2 = A$
negative_passages.docid: 149219
negative_passages.text: If $A$ is a non-square matrix with orthonormal columns, what is $A^+$?
negative_passages.docid: 3599
negative_passages.text: show that if ${a_n} \to a$, and $a>0$, then $\exists N$ such that $a_n>0$ for $n \ge N$.
negative_passages.docid: 60349
negative_passages.text: Schur's theorem and numbers
negative_passages.docid: 152451
negative_passages.text: REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
negative_passages.docid: 113474
negative_passages.text: An $n \times n$ matrix $M$ of integers has the property that $M_{ab} = M_{xy}$ iff $a+b=x+y$. How many distinct elements are there in $M$?
negative_passages.docid: 21782
negative_passages.text: Is $\aleph_0 = \mathbb{N}$?
negative_passages.docid: 129743
negative_passages.text: $A$ be a $2\times 2$ real matrix with trace $2$ and determinant $-3$
negative_passages.docid: 121982
negative_passages.text: Show matrix A is invertible if and only if $a_0 \neq 0$ with $A^n+a_{n-1}A^{n-1}+....+a_1A+a_0I=O$.
negative_passages.docid: 127891
negative_passages.text: If $ a^{2} + b^{2} = c^{2}$ and $c$ is even, prove that $a$ and $b$ are both even.
negative_passages.docid: 140252
negative_passages.text: Matrices - Conditions for $AB+BA=0$
negative_passages.docid: 100627
negative_passages.text: for a $3 \times 3$ matrix A ,value of $ A^{50} $ is
negative_passages.docid: 38635
negative_passages.text: How to prove that the matrix $A^k$ approaches $0$ as $k$ approaches infinity
negative_passages.docid: 25682
negative_passages.text: If $A$ is an $m\times n$ matrix, $B$ is an $n\times m$ matrix and $n<m$, then $AB$ is not invertible.
negative_passages.docid: 52564
negative_passages.text: $m\times n$ matrix with an even number of 1s in each row and column
negative_passages.docid: 33448
negative_passages.text: Proof if $AB+BA=0$ Then atleast one of the matrices are singular.