The rank of an invertible matrix
10911
$A \in M_{n}(\mathbb{R})$ has inverse if and only if it's rank is n.
82925
Let the matrix $A=[a_{ij}]_{n×n}$ be defined by $a_{ij}=\gcd(i,j )$. How prove that $A$ is invertible, and compute $\det(A)$?
44383
Finding rank of a matrix depending on parameter a
63475
Is there any connection between a matrix being invertible and being diagonalizable?
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
19846
Gram matrix invertible iff set of vectors linearly independent
134402
$\mathrm{rank}(A)+\mathrm{rank}(I-A)=n$ for $A$ idempotent matrix
66729
For a square matrix $A$ presence of $n$ linearly independent eigenvectors implies full rank, thereby invertible?
42809
How can we show that $(I-A)$ is invertible?
82688
Least rank of a matrix
30456
The number of $2 × 2$ invertible matrices with entries from field $\mathbb{Z}_p$
71631
About idempotent and invertible matrix
74341
Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
123151
Find the rank of matrix.
19203
Is the rank of a matrix the same of its transpose? If yes, how can I prove it?
97040
Question about an application of the Rank-Nullity theorem
146847
Given a square matrix A of order n, prove $\operatorname{rank}(A^n) = \operatorname{rank}(A^{n+1})$