If  then the matrix A is a/an

This question was previously asked in
NDA (Held On: 21 Apr 2019) Maths Previous Year paper
View all NDA Papers >
  1. Singular matrix
  2. involuntary matrix
  3. Nilpotent matrix
  4. Idempotent matrix

Answer (Detailed Solution Below)

Option 2 : involuntary matrix
Free
UPSC NDA 01/2025 General Ability Full (GAT) Full Mock Test
150 Qs. 600 Marks 150 Mins

Detailed Solution

Download Solution PDF

Concept:

Singular Matrix: Any square matrix of order n is said to be singular if |A| = 0.

Involuntary Matrix: Any square matrix of order n is said to be an involuntary matrix if A2 = I, where I is the identity matrix of order n.

Nilpotent Matrix: Any square matrix of order n is said to be nilpotent matrix if there exist least positive integer m such that Am = O, where O is the null matrix of order n.

Idempotent Matrix: Any square matrix of order n is said to be an idempotent matrix if A2 = A.

Calculation:

Given:

Hence, A is an involuntary matrix as A2 = I.

Latest NDA Updates

Last updated on Jul 8, 2025

->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.

->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

More Matrices Questions

Hot Links: teen patti wink teen patti king teen patti master app teen patti - 3patti cards game downloadable content