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COMEDK · Maths · 21. Matrices

If \(A=\left[\begin{array}{ccc}0 & 1 & -2 \\ -1 & 0 & 3 \\ 2 & -3 & 0\end{array}\right]\) then \(A^{-1}\)

  1. A equal to \(-\dfrac{1}{12}(\operatorname{adj} A)\)
  2. B equal to -12
  3. C doesn't exist
  4. D equal to \(\dfrac{1}{12}(\operatorname{adj} A)\)
Verified Solution

Answer & Solution

Correct Answer

(C) doesn't exist

Step-by-step Solution

Detailed explanation

The matrix \(A\) is given by \(A = \begin{bmatrix} 0 & 1 & -2 \\ -1 & 0 & 3 \\ 2 & -3 & 0 \end{bmatrix}\). Calculate the determinant of \(A\) by expanding along the first row: \(\det(A) = 0(0 - (-9)) - 1(0 - 6) + (-2)(3 - 0)\) \(\det(A) = 0 - 1(-6) - 2(3) = 6 - 6 = 0\). Since…