Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Matrices

NDA 2023 · Mathematics · Matrices

If A=[ array ccc 0 & 3 & 4 -3 & 0 & 5 -4 & -5 & 0 array ] , then...

If A=\left[034−305−4−50\begin{array}{ccc}0 & 3 & 4 \\ -3 & 0 & 5 \\ -4 & -5 & 0\end{array}\right], then which one of the following statements is correct?

Options

  1. A\mathrm{A}^2issymmetricmatrixwithis symmetric matrix with\operatorname\det\left(\mathrm{A}^2\right)=0
  2. BA2A^2 is symmetric matrix with det⁡⁡(A2)≠0\operatorname\det\left(A^2\right) \neq 0
  3. C\mathrm{A}^2isskew−symmetricmatrixwithis skew-symmetric matrix with\operatorname\det\left(\mathrm{A}^2\right)=0
  4. DA2\mathrm{A}^2 is skew-symmetric matrix with det⁡⁡(A2)≠0\operatorname\det\left(\mathrm{A}^2\right) \neq 0

Correct answer

A. \mathrm{A}^2issymmetricmatrixwithis symmetric matrix with\operatorname\det\left(\mathrm{A}^2\right)=0

Step-by-step solution

Since the matrix A is skew symmetric of order 3 (odd) So, |A|=0 and A2\mathrm{A}^2 is symmetric matrix Now ∣A2∣=∣A∣2=0\left|A^2\right|=|A|^2=0 Similarly, ∣A3∣=0,∣A4∣=0\left|A^3\right|=0,\left|A^4\right|=0 Hence \left|4 \mathrm{~A}^4\right|-\left|3 \mathrm{~A}^3\right|+\left|2 \mathrm{~A}^2\right|-|\mathrm{A}|+(-1)^3\left|\mathrm{I}_3\right|=-1
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