By the way Pakistan was not the only muslim country supporting american invasion. All neighbouring islamic countries of afghanistan like Iran, Tajikstan, turkmenistan, Uzbekistan, kergyzstan and Turkey all supported the invasion.
Ahmed Rasheed has written in his book 'Descent into Chaos' that at the time of 9/11, Pakistan had no choice but to vow US. What compelled Pakistan to side with US was kashmir issue. Had Pakistan not dissociated itself from Talibans, Kashmir would have gone. Moreover, future role in the regional politics would have ended also. As india would have emerged as a regional power and pakistan bracketed as terrorist state like north korea.

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Whatever mind can conceive,it can achieve - W.Clement Stone