Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Matrices

NDA 2024 · Mathematics · Matrices

Let X be a matrix of order 3 × 3, Y be a matrix of order 2 × 3 and...

Let X be a matrix of order 3×3,Y3 \times 3, \mathrm{Y} be a matrix of order 2×32 \times 3 and Z be a matrix of order 3×23 \times 2. Which of the following statements are correct? A. (ZY)X(\mathrm{ZY}) \mathrm{X} is defined and is a square matrix of order 3. B. Y(XZ)\mathrm{Y}(\mathrm{XZ}) is defined and is a square matrix of order 2. C. X(YZ)\mathrm{X}(\mathrm{YZ}) is not defined. Select the answer using the code given below.

Options

  1. AAA and BB only
  2. BB and C only
  3. CA and C only
  4. DA,B\mathrm{A}, \mathrm{B} and C

Correct answer

D. A,B\mathrm{A}, \mathrm{B} and C

Step-by-step solution

Since we know that matrix multiplication is only possible when column of first matrix is equal to row of the second matrix. Am×n⋅Bn×p=(AB)m×pA_{m \times n} \cdot B_{n \times p}=(A B)_{m \times p} Thus [Z3×2⋅Y2×3]X3×3=(zyx)3×3\left[\mathrm{Z}_{3 \times 2} \cdot \mathrm{Y}_{2 \times 3}\right] \mathrm{X}_{3 \times 3}=(\mathrm{zyx})_{3 \times 3} and Y2×3⋅[X3×3⋅Z3×2]=(yxz)2×2andx3×3[Y2×3⋅Z3×2]=X3×3⋅(YZ)2×2∵\mathrm{Y}_{2 \times 3} \cdot\left[\mathrm{X}_{3 \times 3} \cdot \mathrm{Z}_{3 \times 2}\right]=(\mathrm{yxz})_{2 \times 2} and \mathrm{x}_{3 \times 3}\left[\mathrm{Y}_{2 \times 3} \cdot \mathrm{Z}_{3 \times 2}\right]=\mathrm{X}_{3 \times 3} \cdot(\mathrm{YZ})_{2 \times 2}\because No. of columns in X=\mathrm{X}= no. of rows in (yz)(\mathrm{yz}) Hence x(yz)x(y z) is not defined.
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 A and B be two square matrices of same order. If A B is a null matrix, then which one… NDA 2024Consider the following in respect of the matrices P=[ array ccc 0 & c & -b -c & 0 & a b &… NDA 2024 Full Matrices list Matrices JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs