The determinant of matrix $A$ is $9a$. Therefore, the correct answer is option (b) $3a$.

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Here are 5 related questions to expand on this:

1. How do you compute the determinant of a 4x4 matrix?
2. What properties of determinants allow factoring out constants like in this case?
3. How would the solution change if the matrix had different elements?
4. Can the determinant of a matrix ever be zero, and under what conditions?
5. How does the determinant affect the invertibility of a matrix?

Tip: When solving matrices, if there's a variable involved, focus on simplifying each minor's determinant step by step to avoid mistakes.