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MHT CET202611 April 2026Evening ShiftMathematicsMatricesActual

If A = bmatrix 0 & 0 & -1 0 & -1 & 0 -1 & 0 & 0 bmatrix then which of the following is true ?

Options

  1. AA^2 = A⁻¹
  2. BA = -( adj A)
  3. CA⁻¹ = A
  4. DA⁻¹ = -A

Correct answer

C. A⁻¹ = A

Step-by-step solution

Given A = bmatrix 0 & 0 & -1 0 & -1 & 0 -1 & 0 & 0 bmatrix Let us calculate A^2 : A^2 = A A = bmatrix 0 & 0 & -1 0 & -1 & 0 -1 & 0 & 0 bmatrix bmatrix 0 & 0 & -1 0 & -1 & 0 -1 & 0 & 0 bmatrix A^2 = bmatrix 0(0) + 0(0) + (-1)(-1) & 0(0) + 0(-1) + (-1)(0) & 0(-1) + 0(0) + (-1)(0) 0(0) + (-1)(0) + 0(-1) & 0(0) + (-1)(-1) + 0(0) & 0(-1) + (-1)(0) + 0(0) (-1)(0) + 0(0) + 0(-1) & (-1)(0) + 0(-1) + 0(0) & (-1)(-1) + 0(0) + 0(0) bmatrix A^2 = bmatrix 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 bmatrix = I Since A^2 = I , multiplying bot

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