How prove that the elementary operations don't change the rank of a matrix
44333
Why do elementary matrix operations not affect the row space of a given matrix?
110381
Prove that if rank(A + B) = rank(A) + rank(B), then col(A) ∩ col(B) = {0}
130268
How to prove that a nilpotent matrix is not invertible?
82688
Least rank of a matrix
156877
Rank-one perturbation proof
119435
Rank of the difference of matrices
130498
Linear algebra proof regarding matrices
146847
Given a square matrix A of order n, prove $\operatorname{rank}(A^n) = \operatorname{rank}(A^{n+1})$
11895
If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$
97040
Question about an application of the Rank-Nullity theorem
70528
Rank of a Matrix Sum
898
Strictly diagonally dominant matrices are non singular
2271
Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix
60736
Looking for an intuitive explanation why the row rank is equal to the column rank for a matrix
87441
Proof involving matrix equation
43000
Show $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A+B)$
6905
Rank of product of a matrix and its transpose