$1.$ Let A be an array of n distinct elements. If i $<$ j and A$[$i$]>$ A$[$j$]$ then the pair $($i$,$ j$)$ is called an inversion of A$.$ Using the concept of inversions, show that the average case time complexity of insertion sort is $($n$2).$ Again, you may look at any source for help, but you may not copy from any source. And please cite your source.