Constructing infinitely many automorphisms of a free group on two generators to itself

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I want to use the universal property of the free group on two generators $F = F(\{a, b\})$ to construct infinitely many automorphisms of $F$, with the restriction that are not they are not inner automorphisms.

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It is well-known that $Aut(F_2)/Inn(F_2)\cong GL_2(\Bbb Z)$, see Bogopolski.