If u, v and w (all positive) are the pth, qth, and rth terms of a GP, then the determinant of the matrix $$\left( {\matrix{ {\ln \,u} & p & 1 \cr {\ln v} & q & 1 \cr {\ln w} & r & 1 \cr } } \right)$$ is

Let matrix B be the adjoint of a square matrix A, I be the identity matrix of same order as A. If k($$\ne$$ 0) is the determinant of the matrix A, then what is AB equal to?

What is the determinant of the matrix $$\left( {\matrix{ x & y & {y + z} \cr z & x & {z + x} \cr y & z & {x + y} \cr } } \right)$$ ?

If A, B and C are the angles of a triangle and $$\left| {\matrix{ 1 & 1 & 1 \cr {1 + \sin A} & {1 + \sin B} & {1 + \sin C} \cr {\sin A + {{\sin }^2}A} & {\sin B + {{\sin }^2}B} & {\sin C + {{\sin }^2}C} \cr } } \right| = 0$$, then which one of the following is correct?