Which of the following is not a possible ordered pair for a matrix with 6 elements

The correct option is (3,1).

An ordered pair for a matrix, denoted as $(r,c)$, represents the number of rows ($r$) and columns ($c$) in the matrix. The total number of elements in a matrix with $r$ rows and $c$ columns is given by the product of the number of rows and the number of columns:
Total Elements = $r\times c$

To find which ordered pair is not possible for a matrix with 6 elements, we calculate the product of the elements in each given ordered pair:
For option (2,3): $2\times 3=6$ elements (Possible)
For option (3,2): $3\times 2=6$ elements (Possible)
For option (1,6): $1\times 6=6$ elements (Possible)
For option (3,1): $3\times 1=3$ elements (Not Possible, as it yields only 3 elements instead of 6)

Therefore, the ordered pair (3,1) cannot represent a matrix containing 6 elements.