Prove T is onto iff $T^t$ is one-to-one.
45416
linear transformation $T$ is onto if and only if $T^*$ is one to one
49592
Show that, if $f:A\to B$ is a function, with $A$ and $B$ being finite sets, and $|A|=|B|$, then $f$ is one to one iff $f$ is onto.
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
52095
Prove either $G=ST$ or |$G|\geq|S|+|T|$
28003
How to prove $A+ A^T$ symmetric, $A-A^T$ skew-symmetric.
76694
Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$
112231
Showing that a one-to-one linear transformation maps a linearly independent set onto a linearly independent set
61884
If $T^n$ is $q$-contractive, $T$ exactly has one fixed point
110643
What are the strategies I can use to prove $f^{-1}(S \cap T) = f^{-1}(S) \cap f^{-1}(T)$?
146023
How to prove that $x^2 - \lfloor x\rfloor^2$ is onto?
115814
If $\operatorname{Re}f^\prime > 0$ on a convex domain, then $f$ is one-to-one.
20110
How to prove $(AB)^T=B^T A^T$
85612
Let functions $ f: A \to B$ and $g: B \to A$, suppose that $ g \circ f = i_A$. Prove that if $f$ is onto, then $g$ is one-to-one
127919
prove that if $E$ is connected and $E \subseteq F \subseteq \overline{E}$, then $F$ is connected.
103801
$xT=x$ iff $x=e$ implies that every $g$ may be written as $x^{-1}(xT)$ for some $x\in G$.
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)