Find the determinant of the matrix A = $\begin{pmatrix} 2 & 3 \\ 1 & 3 \end{pmatrix}$

Analyze the question: You need the determinant of a 2×2 matrix.

Concept: For a matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$, the determinant is

(multiply the main diagonal, then subtract the product of the other diagonal).

Solution:

Here a = 2, b = 3, c = 1, d = 3.

Answer: The determinant is 3, which is option D.

Tip: Remember "main diagonal minus the other diagonal." The most common mistake is adding instead of subtracting, which would give 9 here. Also, keep track of the order, since ad − bc is not the same as bc − ad. Always take the main diagonal first.