Chapter 11.1, Problem 1ED

Suppose that $a$ and $k$ are both saddle values of the matrix

$A=\left[\begin{array}{cccc}a& b& c& d\\ e& f& g& h\\ i& j& k& l\end{array}\right]$

(A) Show that $a$ must equal $k$ after explaining why each of the following must be true $a\le c,c\le k,a\le i$ and $i\ge k$

(B) Show that $c$ and $i$ must equal $k$ as well.