Mathematics : Determinants

Let $\mathrm{A} = \left[\begin{array}{cc}\mathrm{x} + \mathrm{y}& \mathrm{y}\\ 2\mathrm{x}& \mathrm{x} - \mathrm{y}\end{array}\right], \mathrm{B} = \left[\begin{array}{c}2\\ - 1\end{array}\right] \mathrm{and} \mathrm{C} = \left[\begin{array}{c}3\\ 2\end{array}\right]$ If AB = C, then what is the value of the determinant of the matrix A ?

•  - 10

•  - 14

•  - 24

•  - 34

Let p, q and r be three distinct positive real numbers.

If D = $\left|\begin{array}{ccc}\mathrm{p}& \mathrm{q}& \mathrm{r}\\ \mathrm{q}& \mathrm{r}& \mathrm{p}\\ \mathrm{r}& \mathrm{p}& \mathrm{q}\end{array}\right|$ then which one of the following is correct ?

• D < 0

• D ≤ 0

• D > 0

• D ≥ 0