Answer
(a) $12$.
(b) $60.$
Work Step by Step
(a) $$
\left|\begin{array}{rrr}{0} & {b}&{0} \\{a} & {0}&{0}\\{0} & {0}&{c}\end{array}\right|=-\left|\begin{array}{rrr}{a} & {0}&{0}\\{0} & {b}&{0} \\{0} & {0}&{c}\end{array}\right|=-abc=-(1)(4)(-3)=12.
$$
(b) $$
\left|\begin{array}{rrr}{a} & {0}&{1} \\{0} & {c}&{0}\\{b} & {0}&{-16}\end{array}\right|=\left|\begin{array}{rrr}{a} & {0}&{1} \\{0} & {c}&{0}\\{16a+b} & {0}&{0}\end{array}\right|=-c(16a+b)=-(-3)(16+4)=60.
$$
