Decidability. $\lbrace \langle D \rangle \mid \text{$D$ accepts $a^kb^k$ for some $k > 0$}\rbrace$
Corollary 3.19 from "An Introduction to the Theory of Computation": "A language is decidable if and only if some nondeterministic Turing machine decides it."

You can construct a nondeterministic Turing machine, $TM_A$, which is a decider for the language : $A_DFA = \lbrace \langle B,w \rangle \mid \text{$B$ is a DFA accepting $w$}\rangle$.

$TM_A$ works as follows on input $\langle B,w \rangle$, where $B$ is a DFA and $w$ is a string:


Simulate $B$ on input $w$.
If the simulation ends in an accept state, accept. If it ends in an non-accepting state, reject.


Update:
The string $a^kb^k$ is not regular and cannot be accepted by a DFA. A CFG for that string would be something like : $A \to aAb \mid \varepsilon$.