Given an MxN matrix A, the transpose of A can be found by mapping each (i,j) entry of A to the (j,i) position of its transpose. For instance:

Given       |1 2 3|
       A =  |4 5 6|
            |7 8 9| 

for i=j=1, the (1,1) entry of A is 1 and therefore the (1,1) position in Atranspose is 1.
for i-1,j=2 the (1,2) entry of A is 2 and therefore the (2,1) position in Atranspose is 2.
for i=1,j=3 the (1,3) entry of A is 3 and therefore the (3,1) position in Atranspose is 3.
for i=2,j=1 the (2,1) entry in A is 4 and therefore the (1,2) position in Atranspose is 4.
for i=2,j=2 the (2,2) entry in A is 5 and therefore the (2,2) position in Atranspose is 5.
for i=2,j=3 the (2,3) entry in A is 6 and therefore the (3,2) position in Atranspose is 6.

In the end we have:
              |1 4 7|
Atranspose =  |2 5 8|
              |3 6 9|  

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