Given a matrix A such that $a_{ij} = \frac{1}{i + j - 1}$, prove that A is invertible and that $A^{-1}$ has all integer entries.
25159
Why does the inverse of the Hilbert matrix have integer entries?
98323
If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue?
147797
If $A$ is an invertible matrix, then the column span of $A$ equals $F^{n\times1}$
64077
$I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
64747
If $A^m=I$ then A is Diagonalizable
53113
$I-AB$ be invertible $\Leftrightarrow$ $I-BA$ is invertible
109217
Invertibility of the Product of Two Matrices
149287
Prove that $A,B>0$ and $A_{ij}0$
116136
Proof that the inverse of a square matrix is unique
64644
An $r\times r$ submatrix of independent rows and independent columns is invertible (Michael Artin's book).
137920
Proving an equation with invertible matrices
126990
Invertible matrix and inverse matrix
71151
If $a_{ij}=\max(i,j)$, calculate the determinant of $A$
158695
Prove that if $AB$ is invertible then $B$ is invertible.
33477
Proving that if $A$ is a $8\times 8$ matrix over $\mathbb{R}$ and $A^3=A$, then $A$ is diagonalizable.
69980
Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
17584
Integer matrices with integer inverses