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GUJCET · Maths · Determinants

જો \(A=\)\(\left[\begin{array}{cc}2 & -4 \\ -3 & 6\end{array}\right]\) હોય તો, \(A^{-1}\) = _________

  1. A \(\frac{1}{24}\left[\begin{array}{ll}6 & 4 \\ 3 & 2\end{array}\right]\)
  2. B \(\frac{1}{24}\left[\begin{array}{cc}-2 & 4 \\ 3 & -6\end{array}\right]\)
  3. C \(\frac{1}{24}\left[\begin{array}{cc}-6 & 4 \\ 3 & -2\end{array}\right]\)
  4. D અસ્તિત્વ નથી.
Verified Solution

Answer & Solution

Correct Answer

(D) અસ્તિત્વ નથી.

Step-by-step Solution

Detailed explanation

det(\(A\)) \(=\) \((2)(6) - (-4)(-3)\) \(=\) \(12 - 12\) \(=\) \(0\) \(det(A) = 0\) હોવાથી, \(A^{-1}\) અસ્તિત્વ નથી.