Q160 / 270 · NDA 2025 (Phase 2) · Mathematics
What is the value of the determinant of the inverse of the matrix $\begin{pmatrix} -4 & -5 \\ 2 & 2 \end{pmatrix}$?
- Correct answerA$\dfrac{1}{2}$
- B$1$
- C$2$
- D$4$
Solution
Let $A = \begin{pmatrix} -4 & -5 \\ 2 & 2 \end{pmatrix}$.
The determinant of matrix $A$ is given by:
$|A| = (-4)(2) - (-5)(2)$
$|A| = -8 + 10 = 2$
The determinant of the inverse of a matrix is the reciprocal of the determinant of the matrix, i.e., $|A^{-1}| = \dfrac{1}{|A|}$.
$|A^{-1}| = \dfrac{1}{2}$
Answer: $\dfrac{1}{2}$
The determinant of matrix $A$ is given by:
$|A| = (-4)(2) - (-5)(2)$
$|A| = -8 + 10 = 2$
The determinant of the inverse of a matrix is the reciprocal of the determinant of the matrix, i.e., $|A^{-1}| = \dfrac{1}{|A|}$.
$|A^{-1}| = \dfrac{1}{2}$
Answer: $\dfrac{1}{2}$
Hence, the correct answer is option: 'A'.