COMEDK202510 May 2025Morning ShiftMathematicsMatricesActual

If A= [ array ccc 0 & 1 & -2 -1 & 0 & 3 2 & -3 & 0 array ] then A⁻¹

Options

Aequal to - 1 12 ( adj A)
Bequal to -12
Cdoesn't exist
Dequal to 1 12 ( adj A)

Correct answer

C. doesn't exist

Step-by-step solution

The matrix A is given by A = bmatrix 0 & 1 & -2 -1 & 0 & 3 2 & -3 & 0 bmatrix . Calculate the determinant of A by expanding along the first row: (A) = 0(0 - (-9)) - 1(0 - 6) + (-2)(3 - 0) (A) = 0 - 1(-6) - 2(3) = 6 - 6 = 0 . Since (A) = 0 , the matrix A is a singular matrix. A matrix has an inverse if and only if its determinant is non-zero. Therefore, A⁻¹ does not exist. Answer: doesn't exist

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