Prove that `|[a+b,a+2b,a+3b] , [a+3b,a+4b,a+5b] , [a+5b,a+6b,a+7b]|=0`

Prove that: |[a+3b, a+5b, a+7b],[a+4b, a+6b, a+8b], [a+5b, a+7b, a+9b]|= 0

Without expanding the determinant, prove that |{:(a+b, 2a+b, 3a+b),(2a+b, 3a+b, 4a+b), (4a+b, 5a+b, 6a+b):}|=0.

Using properties of determinants, prove that |[a, a+b, a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]|=a^3

Add : 5a + 3b, a - 2b, 3a + 5b

If a :b =3:5 find 2a +3b: 4a+5b

Prove that {:[( a,a+b,a+b+c) ,( 2a,3a+2b,4a+3b+2c),( 3a,6a+3b,10a+6b+3c)]:}=a^(3)

Prove that {:|( a,a+b,a+b+c) ,( 2a,3a+2b,4a+3b+2c),( 3a,6a+3b,10a+6b+3c)|:}=a^(3)