max no of saddle point.. explain

Question

A $n \times n$ matrix is given and an element $a_{ij}$ is called saddle point if all the element in the $i^{th}$ row are less than $a_{ij}$ and all the element in $j^{th}$ column are greater than $a_{ij}$. How many maximum no of saddle point are possible.

1. $2$
2. $3$
3. $n$
4. $1$

Answer 1

Just take the matrix. for 2 point to be saddler the conditions specified will say this. suppose u have two points of a column as saddler point i.e.  q and p .

if u consider 1 as saddler point then it's u must be saying that q>p

while if u have to say 2 also sadller point q<p . only one can happen at a time . make other case yourself and u wll get this .

5 4 3

6 3 2

7 2 1

only 5 is sadler point as considering 6 should say that 6 should be least but 5 is least .