NDA Matrices questions with solutions
Matrix operations and types. 37 questions from our 2016–2025 NDA pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.
NDA 2025
- The system x+y+z=1, x+2y+3z=4, x+3y+kz=6 does NOT have a unique solution when k equals
- Let A be a 2×2 real matrix with A^2=I and A≠± I. Then tr(A) equals
- If a+b+c=0, then the determinant beginvmatrixa&b&c\b&c&a\c&a&bendvmatrix equals
- For a square matrix A of order 3: 1. |2A|=2|A| 2. If A is skew-symmetric, then |A|=0 Which of the statements is/are correct?
- The skew-symmetric part (A-A^T/(2) of A=beginpmatrix1&3\\5&2endpmatrix is
NDA 2024
NDA 2023
- If A=beginpmatrix2&-1\\3&0endpmatrix, the sum of all the entries of A^2 is
- If A=beginpmatrix0&1\\-1&0endpmatrix, then A^2023 equals
- If A=beginpmatrix4&3\\3&2endpmatrix, the sum of the diagonal entries of A^-1 is
- The system x+2y=3, 2x+ky=5 has no solution for k equal to
- If A=beginpmatrix2&3\\1&2endpmatrix, then A^-1 equals
- If A is a square matrix with A^2=A, then (I+A)^2 equals
- Let A=beginpmatrix1&2\\0&1endpmatrix and B=beginpmatrix1&0\\2&1endpmatrix. The determinant of AB-BA is
NDA 2020
- If A is a 3×3 matrix with |A|=4, then the value of |2 adj A| is
- The determinant of every skew-symmetric matrix of even order is zero. 2. Every square matrix can be written as the sum of a symmetric and a…
- The sum of all the elements of the inverse of the matrix beginbmatrix2&1\\5&3endbmatrix is
- The value of beginvmatrix1&1&1\a&b&c\a^2&b^2&c^2endvmatrix for a=1, b=3, c=6 is
- If A=beginbmatrix1&2\\0&1endbmatrix, then A^15 equals
NDA 2019
NDA 2018
- If A is a 3×3 matrix with |A|=3, what is the value of |adj(2A)|?
- What is the sum of the diagonal elements (trace) of the inverse of beginpmatrix2&1\\5&3endpmatrix?
- For square matrices A and B of the same order: 1. (AB)^T=B^TA^T. 2. AB=BA.
- For what value of k does the system x+2y=3, 2x+ky=6 have infinitely many solutions?
- What is the value of the determinant beginvmatrix1&a&b+c\\1&b&c+a\\1&c&a+bendvmatrix?
- The determinant of a skew-symmetric matrix of odd order is zero. 2. Every symmetric matrix is invertible.
NDA 2017
- If A is a 3×3 non-singular matrix with |A|=2, then |3A^-1| equals
- If A=beginpmatrix1&2\\0&1endpmatrix, the top-right entry of A^10 is
- The product of two skew-symmetric matrices of the same order is skew-symmetric. 2. The inverse of a non-singular symmetric matrix is symmetric.
- If A=beginpmatrixcos θ&sin θ\\-sin θ&cos θendpmatrix with θ=(π)/(9), then the (1,1) entry of A^6 is
- How many 2×2 matrices with every entry equal to 0 or 1 are singular?
NDA 2016
- If A is a square matrix such that A^2=A, then (I+A)^3 is equal to
- For A=beginpmatrix2&3\\1&4endpmatrix, the element in the first row and second column of adjA is
- If A=beginpmatrix3&1\\-1&2endpmatrix, then A^2-5A is equal to
- The inverse of an orthogonal matrix is its transpose. 2. If A and B are invertible matrices of the same order, then (AB)^-1=A^-1B^-1.
Other Mathematics topics
Three Dimensional Geometry 48Vector Algebra 60Complex Numbers and Quadratic Equations 35Binomial Theorem 16Sequences and Series 36Quadratic Equations 27Permutations and Combinations 25Statistics 35Probability 27Determinants 13Sets, Relations and Functions 39Binary Number System 11Logarithms 11Inverse Trigonometric Functions 22Trigonometric Functions and Identities 49Trigonometric Equations 16Properties of Triangles 18Heights and Distances 12Straight Lines 43Circles 21Conic Sections 28Limits 23Continuity and Differentiability 16Application of Derivatives 34Derivatives 33Integrals 16Definite Integrals 23Application of Integrals 12Differential Equations 30