Determinants Matrices Question 22
Question: If $ {A^{-1}}= \begin{bmatrix} 1 & -2 \\ -2 & 2 \\ \end{bmatrix} , $ what is det(A)-
Options:
A) $ 2 $
B) $ -2 $
C) $ \frac{1}{2} $
D) $ -\frac{1}{2} $
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Answer:
Correct Answer: D
Solution:
- [d] We know that det $ (A)=\frac{1}{\det ({A^{-1}})} $
$ {A^{-1}} \begin{bmatrix} 1 & -2 \\ -2 & 2 \\ \end{bmatrix} $
$ \Rightarrow | {A^{-1}} |= \begin{vmatrix} & 1-2 \\ & -22 \\ \end{vmatrix} =2-4=-2 $
$ \Rightarrow \det (A)=-\frac{1}{2} $
BETA
