Using the property of determinant and without expanding prove that \(\left| {\begin{array}{*{20}{c}} 2&7&{65} \\ 3&8&{75} \\ 5&9&{86} \end{array}} \right| = 0\)
Find the minor of element 6 in the determinant \(\Delta=\left|\begin{array}{lll} {1} & {2} & {3} \\ {4} & {5} & {6} \\ {7} & {8} & {9} \end{array}\right|\)
If a, b, c, are in A.P, then the determinant \(\left|\begin{array}{ccc} {x+2} & {x+3} & {x+2 a} \\ {x+3} & {x+4} & {x+2 b} \\ {x+4} & {x+5} & {x+2 c} \end{array}\right|\) is