Question:
The value of the determinant of the inverse of the matrix \(\begin{bmatrix} -4 & -5\\ 2 & 2 \end{bmatrix}\) is
The value of the determinant of the inverse of the matrix \(\begin{bmatrix} -4 & -5\\ 2 & 2 \end{bmatrix}\) is
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Determinant of inverse = reciprocal of determinant.
Updated On: Apr 30, 2026
- $\frac{1}{4}$
- $\frac{1}{2}$
- $-\frac{1}{4}$
- $1$
- $2$
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The Correct Option is B
Solution and Explanation
Concept:
\[
\det(A^{-1}) = \frac{1}{\det(A)}
\]
Step 1: Find determinant of matrix
\[ \det(A) = (-4)(2) - (-5)(2) = -8 + 10 = 2 \]
Step 2: Inverse determinant
\[ \det(A^{-1}) = \frac{1}{2} \] Final Conclusion:
Option (B)
Step 1: Find determinant of matrix
\[ \det(A) = (-4)(2) - (-5)(2) = -8 + 10 = 2 \]
Step 2: Inverse determinant
\[ \det(A^{-1}) = \frac{1}{2} \] Final Conclusion:
Option (B)
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