$AA^{T}B=AA^{T}C $ implies $A^{T}B=A^{T}C$
49330
If for two suitable matrices $B$ and $C$, $AA^TB=AA^TC$ can we conclude that $A^TB=A^TC$?
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
140446
Prove that $A \smallsetminus (A \smallsetminus B) = A \cap B$
15416
A weak converse of $AB=BA\implies e^Ae^B=e^Be^A$ from "Topics in Matrix Analysis" for matrices of algebraic numbers.
13026
Prove that if AB=I_m, then rk(A)=rk(B).
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
139841
Proving $A\setminus(B\setminus C)$ is not equal to $(A\setminus B)\setminus C$
67717
$A \oplus B = A \oplus C$ imply $B = C$?
83713
If $z,w\in \mathbb{C}^{\times}$, then $|z+w|=|z|+|w|$ iff $w=tz$ for some $t\gt 0$
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
124320
$a,b,c>0 \text{ s.t. }a+b+c=1 \implies \sqrt{ab+c}+\sqrt{bc+a}+\sqrt{ca+b} \ge 1+ \sqrt{ab}+\sqrt{bc}+\sqrt{ca}$
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$
94383
Prove that $A^TD-C^TB=I$
130137
How to define a Bijection between $(A^B)^C$ and $A^{B \times C}$
112707
Must $Q^\mathsf{T}Q = I$ if $(Qx)^\mathsf{T}(Qx) = x^\mathsf{T}x$
68258
Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$