Official solution
Given, \[\left[ {A \wedge \left( {A \to B} \right)} \right] \to B\]
= \[A \wedge \left( { \sim A \vee B} \right) \to B\]
= \[\left[ {\left( {A \wedge \sim A} \right) \vee \left( {A \wedge B} \right)} \right] \to B\]
= \[\left( {A \wedge B} \right) \to B\]
= \[{ \sim A \vee \sim B \vee B}\]
= t
Hence, \[\left[ {A \wedge \left( {A \to B} \right)} \right] \to B\] is a tautology.