Show that $rank(A)+rank(B) \leq n$, when $A,B$ are $2$ matrices of size $n \times n$, and $AB=0$
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
140252
Matrices - Conditions for $AB+BA=0$
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
19203
Is the rank of a matrix the same of its transpose? If yes, how can I prove it?
27474
A square matrix $n \times n$ is an invertible matrix iff the rank of the matrix is $n$.
146984
Prove: Full Rank and a solution os linear system
48660
Proof that determinant rank equals row/column rank
110381
Prove that if rank(A + B) = rank(A) + rank(B), then col(A) ∩ col(B) = {0}
45532
Let $A$ be a $n\times n$ matrix with entries $a_{ij}=i+j $ . Calculate rank of $A$
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
69980
Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
34043
A rank-one matrix is the product of two vectors
25870
Prove that $0 \leq ab + ac + bc - abc \leq 2.$
75117
$\mathrm{rank}(AB-BA)=1$ implies $A$ and $B$ are simultaneously triangularisable
33451
Sylvester rank inequality: $\operatorname{rank} A + \operatorname{rank}B \leq \operatorname{rank} AB + n$