Show $\det(A + B) \geq 0$ implies $\det(A^k + B^k) \geq 0$ if $A, B$ commute
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
59396
Show that the rank of $A+B$ is no more than the sum of the ranks of $A$ and $B$
65162
Show that $\dim H^0(\mathbb{P}^n, \mathcal{O}_{\mathbb{P}^n}(m)) = {n + m \choose n}$ if $m \geq 0$, and $0$ otherwise.
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
50266
In the following figure prove that: $AK||BC$
38448
Show that a simple inequality holds: $a<b$ implies $\frac ab < \frac{a+1}{b+1}$
116389
If $\exp(t(A + B)) = \exp(tA) \exp(tB)$ for all $t \geq 0$ then $A,B$ commute
123483
Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$
69980
Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
88746
Positive definiteness of the matrix $A+B$
77192
How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?
158355
If $A$ commutes with $B$ and $B$ commutes with $C$, then $A$ commutes with $C$
95852
Prove that $(a+b)(b+c)(c+a) \ge8$
110381
Prove that if rank(A + B) = rank(A) + rank(B), then col(A) ∩ col(B) = {0}
59513
For $a, b \geq 0$, $0 < x < 1$, show $(a+b)^x \leq a^x + b^x$
149287
Prove that $A,B>0$ and $A_{ij}0$
10236
Show that $a^n \mid b^n$ implies $a \mid b$