Basic operations on adjoint operators

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How do you prove :

$a^{\dagger}b^{\dagger}ba=a^{\dagger}ab^{\dagger}b$ knowing that $[b,b^{\dagger}]=[a,a^{\dagger}]=1$ and where $^{\dagger}$ denotes the adjoint.

do you need extra properties on $a$ and $b$ or is it straight forward?