If A=≤ft[{array}{ccc}0 & 1 & -2 \\ -1 & 0 & 3 \\ 2 & -3 & 0{array}] then A^{-1}

Correct Answer is : doesn't exit

Correct Answer is : doesn't exit

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COMEDK 2025 Morning Solved Paper

Question : 150 of 180

Marks: +1, -0

A=\left[\begin{array}{ccc}0 & 1 & -2 \\ -1 & 0 & 3 \\ 2 & -3 & 0\end{array}\right]

A^{-1}

Solution:

Concept:

For a

3 \times 3

skew‑symmetric matrix, the determinant is always zero, so the matrix is singular and its inverse does not exist.

Explanation:

The given matrix

A

is skew‑symmetric because

A^T = -A

For any square matrix,

\det(A^T) = \det(A)

Using

A^T = -A

, we get

\det(A) = \det(-A) = (-1)^3 \det(A) = -\det(A)

Thus

2\det(A) = 0

, so

\det(A) = 0

A matrix with zero determinant is singular and cannot be inverted.

Answer:

Option D:

A^{-1}

does not exist.

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