If for the matrix A, A³ = I then A⁻¹= __________.

Question

Question

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NIELIT Scientific Assistant IT 5 Dec 2021 Official Paper

Answer 1

The correct answer is option 1: A²

Key Points

Given: \( A^3 = I \), where \( I \) is the identity matrix.
This means: \( A \cdot A \cdot A = I \).
We want to find \( A^{-1} \), the inverse of A.
Multiply both sides of \( A^3 = I \) by \( A^{-1} \):
- \( A^2 \cdot A \cdot A^{-1} = I \cdot A^{-1} \)
- \( A^2 \cdot I = A^{-1} \Rightarrow A^2 = A^{-1} \)

Therefore, the inverse of A is A².

Hence, the correct answer is: option 1: A²

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