If A=≤ft[{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0{array}] then which of the following is true ?

Correct Answer is : A−1=AA^{-1}=AA−1=A

Correct Answer is : A−1=AA^{-1}=AA−1=A

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MHTCET 11 Apr 2026 Shift 2 Paper

Question : 115 of 150

Marks: +1, -0

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

then which of the following is true ?

Solution:

Concept:

A^2 = I

, then

A

is its own inverse, so

A^{-1} = A

Explanation:

The given matrix is:

A = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{bmatrix}

Compute

A^2 = A \cdot A

A^2 = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{bmatrix} \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{bmatrix}

Multiplying row by column gives:

A^2 = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} = I

Thus,

A \cdot A = I

By definition, if

A \cdot B = I

, then

B = A^{-1}

Here,

B = A

itself.

Therefore,

A^{-1} = A

Hence, option C is true.

Answer:

Option C:

A^{-1} = A

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