If `|[a, p, x],[ b, q, y], [c, r, z]|=16 ,` then the value of `|[p+x, a+x, a+p], [q+y ,b+y, b+q],[ x+z, c+z, c+r]|` is 4 (b) 8 (c) 16 (d) 32

Explanation

$$\left|\begin{array}{lll}p+q & a+x & a+p \\ q+y & b+y & b+q \\ x+z & c+z & c+r\end{array}\right|$$
$$c_{1} \rightarrow c_{1}+c_{2}+c_{3}$$
$$\left|\begin{array}{lll}2 a+2 p+q+x & a+x & a+p \\ 2 b+2 q+y+b & b+y & b+q \\ 2 c+x+2 z+r & c+z & c+r\end{array}\right|$$
$$2\left|\begin{array}{lll}\mathrm{a} & \mathbf{x} & \mathrm{p} \\ \mathrm{b} & \mathbf{y} & \mathrm{q} \\ \mathbf{c} & \mathbf{z} & \mathrm{r}\end{array}\right|+\left|\begin{array}{lll}2 \mathrm{p}+\mathbf{q}+\mathbf{x} & \mathrm{a} & \mathrm{a} \\ 2 \mathrm{q}+\mathbf{y}+\mathbf{b} & \mathrm{b} & \mathrm{b} \\ \mathrm{x}+2 \mathrm{z}+\mathbf{r} & \mathrm{c} & \mathbf{c}\end{array}\right|$$
$$2\left|\begin{array}{lll}\mathrm{a} & \mathbf{x} & \mathrm{p} \\ \mathrm{b} & \mathrm{y} & \mathrm{q} \\ \mathrm{c} & \mathbf{z} & \mathbf{r}\end{array}\right|+0$$
$$2 \times 16=32$$