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GUJCET · Maths · Determinants
If \(A=\left[\begin{array}{cc}2 & -4 \\ -3 & 6\end{array}\right]\) then, \(A^{-1}=\) _________ .
- A \(\frac{1}{24}\left[\begin{array}{ll}6 & 4 \\ 3 & 2\end{array}\right]\)
- B \(\frac{1}{24}\left[\begin{array}{cc}-2 & 4 \\ 3 & -6\end{array}\right]\)
- C \(\frac{1}{24}\left[\begin{array}{cc}-6 & 4 \\ 3 & -2\end{array}\right]\)
- D does not exist
Answer & Solution
Correct Answer
(D) does not exist
Step-by-step Solution
Detailed explanation
\(det(A) = (2)(6) - (-4)(-3) = 12 - 12 = 0\) Since \(det(A) = 0\), \(A^{-1}\) does not exist.
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