Transpose an n*m matrix to an m*n matrix 
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Assume that we have the following 5 * 3 matrix in A1 to C5. 

1,3,4
5,2,1
3,2,3
4,3,0
7,1,2

Since it is a 5 by 3 matrix, it will be a 3 by 5 matrix after transpose, 
we highlight a 3 by  5 area  then enter the following equation 

 =transpose(A1:C5)

   then hit Ctrl-Shift-Enter

 If everything is fine, after we hit three keys (Ctrl-Shift-Enter), 
   we will see 

   {=TRANSPOSE(A1:C5)}

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For a large data set, how to highlight it?
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 Move our curser to the data set, then hit Ctrl-A

 Note: here we assume that there is not black row or 
         column in our data set. 

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Explanation of matrix multiplication
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   We have two matrix A and B. Assume that the dimensions of A is n*m 
        while it is m*k for matrix B. 

   For A, each item, we could use a(i,j), i from 1 to n and j from 1 to m. 
                a11,  a12,   ....,    a1m
                a2,   a22,   ....,    a2m
      A =       ...    ....   .....    ..

                an1,   an2    .....     ann

   For B, each item, we could use b(i,j) where i from 1 to m and j from 1 to k. 
                B11,   B12,   ....,    B1k
                B21,   B22,   ....,    B2k
      B =       ...    ....   .....    ..

                Bm1,   Bm2    .....    Bmk

   Let's call their product as c, i.e, C= A * B
   For C, each item, we could use c(i,j) where i from 1 to n and j from 1 to m. 
                C11,   B12,   ....,    B1k
                C21,   B22,   ....,    B2k
      C =       ...    ....   .....    ..

                Cn1,   Bn2    .....    Bnk

   The following formula is the most important !!!!
       In words, for the ith row and jth column in final C matrix, 
           its value is the product of ith row of A times the jth column of B. 

       c(i,j) = a(i,1)* b(1,j) + a(i,2) *b(2,j) +  ..... + a(i,m)*b(m,j) 

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