The determinant of the $2 \times 2$ matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ is:

For a $2 \times 2$ matrix: $\det \begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad - bc$. Geometric meaning: this is the signed area of the parallelogram spanned by the two column vectors $\binom{a}{c}$ and $\binom{b}{d}$. Use: the matrix is invertible if and only if its determinant is non-zero. The inverse formula in $2 \times 2$ is $\dfrac{1}{ad - bc}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$. Option D is the trace (sum of diagonal elements), not the determinant.