$\left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}2&7&{65}\\3&8&{75}\\5&9&{86}\end{array}} \right| = 0$

L.H.S. $=$ $\left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}2&7&{65}\\3&8&{75}\\5&9&{86}\end{array}} \right|$
Applying ${C_1} \to {C_1} + 9{C_2}$

, we get
$\left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}{65}&7&{65}\\{75}&8&{75}\\{86}&9&{86}\end{array}} \right| = 0$

[If any two rows or columns of a determinant are identical (all corresponding elements are same), the value of determinant is zero].