Let a,b,c be such that b(a+c) `ne ` 0. If
`|{:(a,a+1,a-1),(-b,b+1,b-1),(c,c-1,c+1):}|+|{:(a+1,b+1,c-1),(a-1,b-1,c+1),((-1)^(n+2)a,(-1)^(n+1)b,(-1)^(n)c):}|`=0 then the value of n is

Options

A. zero
B. any even integer
C. any odd integer
D. any integer

Answer

3

Explanation

`|{:(a,,a+1,,a-1),(-b,,b+1,,b-1),(c,,c-1,,c+1):}|+(-1)^(n) |{:(a+1,,b+1,,c-1),(a-1,,b-1,,c+1),(a,,-b,,c):}|`
`= |{:(a,,a+1,,a-1),(-b,,b +1,,b-1),(c,,c-1,,c+1):}|+(-1)^(n) |{:(a+1,,a-1,,a),(b+1,,b-1,,c+1),(c-1,,c+1,,c):}|`
`= |{:(a,,a+1,,a-10),(-b,,b+1,,b-1),(c,,c-1,,c+1):}|+(-1)^(n+2) |{:(a,,a+1,,a-1),(-b,,b+1,,b-1),(c,,c-1,,c+1):}|`
this is eqaul to zero only in n+2 i sodd i.e., n is an odd integer