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MHT CET202618 April 2026Morning ShiftMathematicsMatricesActual

Let A = bmatrix & - & 0 & & 0 0 & 0 & 1 bmatrix . If B = adj ,A , then the matrix B⁻¹ is equal to...

Options

  1. AI
  2. BA⁻¹
  3. C-A
  4. DA

Correct answer

D. A

Step-by-step solution

The determinant of matrix A is given by |A| = ( - 0) - (- )( - 0) + 0 |A| = ^2 + ^2 = 1 We know the property of adjoint of a matrix: A( adj ,A) = |A|I Substituting |A| = 1 , we get A( adj ,A) = I adj ,A = A⁻¹ It is given that B = adj ,A , so B = A⁻¹ Taking the inverse on both sides, we obtain B⁻¹ = (A⁻¹)⁻¹ = A Answer: A

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