Matrices — Easy JEE math MCQ
If $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$, then $\det(3A)$ equals:
- A. $-18$
- B. $-6$
- C. $18$
- D. $-2$
Solution
For a $n \times n$ matrix $A$: $\det(kA) = k^n \det(A)$
Here $n = 2$ and $k = 3$.
First, find $\det(A)$:
$$\detA. = 1 \times 4 - 2 \times 3 = 4 - 6 = -2$$
Therefore:
$$\det(3A) = 3^2 \times \detA. = 9 \times (-2) = -18$$