Matrices Test

Matrices

This is Matrices Test-01 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The number of all possible matrices of order \(3 \times 3\) with each entry 0 if 1 is
  • A
    18
  • B
    512
    Correct
  • C
    81
  • D
    none of these
2
\({I_2}\) is the matrix
  • A
    \(\left[ {\begin{array}{*{20}{c}} 1&0 \\ 0&1 \end{array}} \right]\)
    Correct
  • B
    \(\left[ {\begin{array}{*{20}{c}} 1&1 \\ 1&1 \end{array}} \right]\)
  • C
    \(\left[ {\begin{array}{*{20}{c}} 0&1 \\ 1&0 \end{array}} \right]\)
  • D
    \(\left[ {\begin{array}{*{20}{c}} 1&1 \\ 0&1 \end{array}} \right]\)
3
If A is a matrix of order\(3{\text{ }} \times {\text{ }}4\) , then each row of A has
  • A
    7 elements.
  • B
    4 elements
    Correct
  • C
    3 elements
  • D
    12 elements
4
If P is of order \({\text{2 }} \times {\text{ 3}}\) and Q is of order \(3{\text{ }} \times {\text{ 2}}\), then PQ is of order
  • A
    \({\text{2 }} \times {\text{ 3}}\)
  • B
    \({\text{2 }} \times {\text{ 2}}\)
    Correct
  • C
    \(3{\text{ }} \times {\text{ 3}}\)
  • D
    \(3{\text{ }} \times {\text{ 2}}\)
5
The number of all the possible matrices of order \({\text{2 }} \times {\text{ 2}}\) with each entry 0, 1 or 2 is
  • A
    81
    Correct
  • B
    none of these.
  • C
    12
  • D
    64
6
If \(\left[ {\begin{array}{*{20}{c}} 0&0&0 \\ 0&0&0 \\ 0&1&0 \end{array}} \right]\) then A is
  • A
    an idempotent matrix
  • B
    a nilpotent matrix
    Correct
  • C
    none of these
  • D
    an invertible matrix
7
If A and B are symmetric matrices of the same order, then
  • A
    A – B is a skew-symmetric matrix
  • B
    AB + BA is a symmetric matrix
    Correct
  • C
    AB is symmetric matrix
  • D
    AB – BA is a symmetric matrix
8
A square matrix \(A = {\left[ {{a_{ij}}} \right]_{n \times n}}\) is called a diagonal matrix if \({a_{ij}} = 0\) for
  • A
    \(I{\text{ }} \ne {\text{ }}j\)
    Correct
  • B
    \(I{\text{ }} < {\text{ }}j\)
  • C
    \(\begin{array}{*{20}{l}} {I{\text{ }} = {\text{ }}j} \end{array}\)
  • D
    \(I{\text{ }} > {\text{ }}j\)
9
If a square matrix A has two identical rows or columns , then det.A is :
  • A
    none of these.
  • B
    0
    Correct
  • C
    -1
  • D
    1
10
The order of [x y z] \(\left[ {\begin{array}{*{20}{c}} a&h&g \\ h&b&f \\ g&f&c \end{array}} \right]\left[ {\begin{array}{*{20}{c}} x \\ y \\ z \end{array}} \right]\)is
  • A
    \(1 \times 1\)
    Correct
  • B
    \(3 \times 1\)
  • C
    \(3 \times 3\)
  • D
    \(1 \times 3\)
11
If a matrix A is symmetric as well as skew symmetric then A is a
  • A
    diagonal matrix
  • B
    unit matrix
  • C
    none of these.
  • D
    null matrix
    Correct
12
A square matrix A is called idempotent if
  • A
    \({A^2} = A\)
    Correct
  • B
    \({A^2} = I\)
  • C
    \({A^2} = O\)
  • D
    2A=I
13
If \(\left[ {\begin{array}{*{20}{c}} a&b \\\\\\ c&{ - a} \end{array}} \right]\)is a square root of the \(2 \times 2\;\) identity matrix, then a, b, c satisfy the relation\(\)
  • A
    \(1 - {a^2} + bc = 0\)
  • B
    \(1 + {a^2} + bc = 0\)
  • C
    \({a^2} + bc = 1\)
  • D
    \(1 + {a^2} - bc = 0\)
Answer
Not Available
14
If A and B are invertible matrices of the same order, then \({(AB)^{ - 1}}\)is equal to
  • A
    \(A{B^{ - 1}}\)
  • B
    \({A^{ - 1}}B\)
  • C
    \({B^{ - 1}}{A^{ - 1}}\)
    Correct
  • D
    \({A^{ - 1}}{B^{ - 1}}\)
15
If \(\left[ {\begin{array}{*{20}{c}} 0&0&0&0 \\ 0&0&0&0 \\ 1&0&0&0 \\ 0&1&0&0 \end{array}} \right]\), then
  • A
    \({A^2} = I\)
  • B
    none of these.
  • C
    \({A^2} = O\)
    Correct
  • D
    \({A^3} = O\)