Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Matrices

NDA 2012 · Mathematics · Matrices

If A is a square matrix such that A^2=1 where I is the identity...

If AA is a square matrix such that A2=1A^2=1 where II is the identity matrix, then what is A−1\mathrm{A}^{-1} equal to?

Options

  1. AA+1
  2. BNull matrix
  3. CA
  4. DTranspose of A

Correct answer

C. A

Step-by-step solution

A2=I⇒A2A−1=IA−1A=A−1.\begin{aligned} \mathrm{A}^2 & =\mathrm{I} \\ \Rightarrow \quad \mathrm{A}^2 \mathrm{ A}^{-1} & =\mathrm{IA}^{-1} \\ \mathrm{ A} & =\mathrm{A}^{-1}.\end{aligned}
Practice Matrices on Quantrex Academy →

More from Matrices

Consider the following statements : I. If n× n(n > 1) matrix is symmetric, then its… NDA 2026If M is a square matrix such that M^3=M , then how many values of |M| are possible ? NDA 2026If M_k= bmatrix k & k-1 k-1 & k bmatrix where k is a natural number, then what is… NDA 2026If M^ T is the transpose of a 2×2 matrix M , then which of the following is/are correct ?… NDA 2026Consider the following in respect of non-singular matrices A and B : I. (AB)^ -1 = A^ -1… NDA 2025For the following two (02) items: Let A = pmatrix θ & θ - θ & θ pmatrix . What is [adj\… NDA 2025Consider the following statements about the matrix M = pmatrix 71 & 23 & 48 57 & 28 & 29… NDA 2025If [x \ 1 \ 1] pmatrix 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 pmatrix pmatrix 1 1 x pmatrix = [45]… NDA 2025If A = pmatrix 1 & 2 & 2 2 & 1 & 2 2 & 2 & 1 pmatrix , then what is A^2 - 4A equal to? NDA 2025If A = pmatrix y & z & x z & x & y x & y & z pmatrix where x , y , z are integers, is an… NDA 2025If A = pmatrix x & y & z y & z & x z & x & y pmatrix where x , y , z are integers, is an… NDA 2025For the following two (02) items: Let A = pmatrix θ & θ - θ & θ pmatrix . What is the… NDA 2025What is the value of the determinant of the inverse of the matrix pmatrix -4 & -5 2 & 2… NDA 2025If f(θ) = pmatrix θ & θ - θ & θ pmatrix , then what is \ f(π)\ ^2 equal to? NDA 2025Let X be a matrix of order 3 × 3, Y be a matrix of order 2 × 3 and Z be a matrix of order… NDA 2024Let A and B be two square matrices of same order. If A B is a null matrix, then which one… NDA 2024 Full Matrices list Matrices JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs