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

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NIELIT Scientific Assistant CS 5 Dec 2021 Official Paper
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  1. A2
  2. A3 
  3. A
  4. None of these

Answer (Detailed Solution Below)

Option 1 : A2
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Detailed Solution

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Explanation:
We are given that A3 = I, where I is the identity matrix.

This implies: A × A × A = I

Now, multiply both sides by A-1 on the right:

A × A × A × A-1 = I × A-1

⟹ A × A = A2 = A-1

⟹ A-1 = A2

Final Answer: Option 1) A2 ✅

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Latest NIELIT Scientific Assistant Updates

Last updated on Feb 20, 2025

-> A total number of 113 revised vacancies have been announced for the post of Scientific Assistant in Computer Science (CS), Information Technology (IT), and Electronics & Communication (EC) streams.

-> Online application form, last date has been extended up to from 17th April 2025.

->The NIELT has revised the Essential Qualifications for the post of Scientific Assistant. Candidates must possess (M.Sc.)/ (MS)/ (MCA) / (B.E.)/ (B.Tech) in relevant disciplines.

 

-> The NIELIT Scientific Assistant 2025 Notification has been released by the National Institute of Electronics and Information Technology (NIELIT).

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