Prove that rank(A) = rank(A|C)
39800
Existence of solution for a linear system mod 2
21758
Rank of the $n \times n$ matrix with ones on the main diagonal and $a$ off the main diagonal
80009
Prove that $| |a|-|b| | \le |a-b|$
151038
How to prove (A v B), (A → C), (B → D) therefore (C v D)
29935
If $a, b, c, d>0$ and $abcd=1$ prove that an inequality holds true
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
27248
If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
146847
Given a square matrix A of order n, prove $\operatorname{rank}(A^n) = \operatorname{rank}(A^{n+1})$
147014
Matrix algebra: If $A^2=0$, Proof rank(A) $\le \frac{n}{2}$
37162
Prove that matrices have equal rank.
130799
Matrix of rank 1; show that $A^2=cA$ for some scalar $c$.
64517
Prove that row rank of a matrix equals column rank
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
150738
Proof of $(A - B) - C = A - (B \cup C)$
137148
If $A=\left( \begin{array}{ccc} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{array} \right)$, find the rank of $A+A^2+A^3$
156877
Rank-one perturbation proof