query: Cool simple solution to: $-A^2$ is not the identity matrix
positive_passages.docid: 146243
positive_passages.text: Does there exist a matrix $\mathbf{A}\in\mathbb{R}^{3\times3}$ such that $\mathbf{A}^{2}=-\mathbf{I}$?
negative_passages.docid: 103665
negative_passages.text: Product of matrices of different order is not invertible
negative_passages.docid: 128043
negative_passages.text: $A^n=0$ for $A$ nilpotent without the use of minimal polynomial
negative_passages.docid: 127664
negative_passages.text: Inverse elements in the absence of identities/associativity.
negative_passages.docid: 70576
negative_passages.text: Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
negative_passages.docid: 109736
negative_passages.text: For a 2x2 matrix A satisfying $A^k=I$, compute $e^A$
negative_passages.docid: 54118
negative_passages.text: Proving Eigenvalue squared is Eigenvalue of $A^2$
negative_passages.docid: 49855
negative_passages.text: Need a matrix to seventh power which is the identity but the original is not or the negative identity
negative_passages.docid: 130268
negative_passages.text: How to prove that a nilpotent matrix is not invertible?
negative_passages.docid: 97990
negative_passages.text: Why can the row-reduced echelon matrix $R$ only be identity matrix?
negative_passages.docid: 86015
negative_passages.text: $\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
negative_passages.docid: 57981
negative_passages.text: Alternative proof of $a\times0= 0$
negative_passages.docid: 60990
negative_passages.text: Tricky operator identity: $[L^2,[L^2,\vec{r}]]=2 \hbar ^2 \{ L^2, \vec{r}\}$?
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: 156438
negative_passages.text: Find a matrix equation equivalent to $A^TPA+P=I$
negative_passages.docid: 77587
negative_passages.text: Cross product: matrix transformation identity
negative_passages.docid: 156989
negative_passages.text: Proof that Hadamard matrices of order $4k+2$ don't exist