Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Matrices

NDA 2019 · Mathematics · Matrices

If A= ( array ll 1 & 2 2 & 3 3 & 4 array ) and B=( array ll 1 & 2 2...

If A=A=\left(122334\begin{array}{ll}1 & 2 \\ 2 & 3 \\ 3 & 4\end{array}\right)and B=\left(1221\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right), then which one of the following is correct?

Options

  1. ABoth AB and BA exist
  2. BNeither AB nor BA exists
  3. CAB exists but BA does not exist
  4. DAB does not exist but BA exists

Correct answer

C. AB exists but BA does not exist

Step-by-step solution

A=A=\left[122334\begin{array}{ll}1 & 2 \\ 2 & 3 \\ 3 & 4\end{array}\right] ; B=\left[1221\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right] Order of A=3×2A=3 \times 2 Order of B=2×2∴B=2 \times 2\therefore by fundamental properties we can say ABA B exists while BAB A does not exist.
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