Consider the matrix $M=\left[\begin{array}{ccc}2 & 1 & 1 \\ 1 & 3 & 0 \\ -1 & a & b\end{array}\right]$.
Which of the following options is/ are TRUE if $\operatorname{det}(M) \neq 0$ ?
- A
$a=-\frac{1}{2}$ and $b=-\frac{1}{2}$
- B
$a=\frac{1}{2}$ and $b=\frac{1}{2}$
- C
$a=-3$ and $b=0$
- D
$a=\frac{1}{2}$ and $b=-3$
✓ Correct answer: B
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