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MHT CET202620 April 2026Evening ShiftMathematicsMatricesActual

If A = bmatrix 1 & -5 -2 & 4 bmatrix , then A⁻¹ =

Options

  1. A- 1 6 bmatrix -4 & 5 2 & -1 bmatrix
  2. B1 14 bmatrix -1 & 5 2 & -4 bmatrix
  3. C1 14 bmatrix 4 & 5 2 & 1 bmatrix
  4. D- 1 6 bmatrix 4 & 5 2 & 1 bmatrix

Correct answer

D. - 1 6 bmatrix 4 & 5 2 & 1 bmatrix

Step-by-step solution

Given A = bmatrix 1 & -5 -2 & 4 bmatrix The determinant of A is |A| = (1)(4) - (-5)(-2) = 4 - 10 = -6 The adjoint of A is obtained by interchanging the diagonal elements and changing the signs of the off-diagonal elements: adj (A) = bmatrix 4 & 5 2 & 1 bmatrix The inverse of the matrix is given by A⁻¹ = 1 |A| adj (A) A⁻¹ = - 1 6 bmatrix 4 & 5 2 & 1 bmatrix

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