The product of `13xx5` matrix & `5xx13` matrix contains a variable entry `x` in exactly 2 places. If `D(x)` is the determinant of the matrix product such that `D(0)=1, D(-1)=1`& `D(2)=7` which of the following is/are correct?

Options

A. `D(-2)=3`
B. `D(1)=3`
C. `D(-3)=7`
D. `D(1)=2`

Answer

A, B, C

Explanation

`D(x)` can at most be polymial of degree 2
`D(x)=ax^(2)+bx+c`
`D(x)=x^(2)+x+1`
`D(1)=3`
`D(-2)=4-2+1=3`
`D(-3)=9-3+1=7`