Question

Evaluate the following determinant:

`|(0, "a", -"b"),(-"a", 0, -"c"),("b", "c", 0)|`

Answer 1

`|(0, "a", -"b"),(-"a", 0, -"c"),("b", "c", 0)|`

= `0|(0, -"c"),("c", 0)| -"a"|(-"a", - "c"),("b", 0)| -"b"|(-"a", 0),("b", "c")|`

= 0 – a (0 + bc) – b(– ac – 0)

= – a(bc) – b (– ac)

= – abc + abc

= 0