From wikipedia (emphasis mine):
A saddle point is an element of the matrix which is both the largest
element in its column and the smallest element in its row.
You can determine it by going through the matrix in row-order and:
when you are done with this you can compare if an index occurs in both at the same time so that you have an index which is both the column-max and row-min.
Note: your example-matrix does not have any saddle points according to wikipedia's definition.
