What is the adjoint of |01> in quantum computing?

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Homework Statement
Is <01| the adjoint of |01>?
Relevant Equations
adjoint(|01>)
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Is there a way for you to check if ## \langle 0 1 |## is the "adjoint" of ## | 0 1 \rangle##?
 
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There's what I did in the show my work section; I'm asking if it's correct.