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Matrices

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Concept, notation, order, equality, types of matrices, zero and identity matrix

Subtopic

Concept, notation, order, equality, types of matrices, zero and identity matrix under Matrices for Grade 12 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Two matrices Am×nA_{m \times n} and Bp×qB_{p \times q} can be equal only if:

    A.

    m=pm=p and n=qn=q

    B.

    m=qm=q and n=pn=p

    C.

    m×n=p×qm \times n = p \times q

    D.

    m=nm=n and p=qp=q

  2. 2.

    The zero matrix of order 2×32 \times 3 is written as:

    A.

    [000000]\begin{bmatrix} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{bmatrix}

    B.

    [000000]\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}

    C.

    [00]\begin{bmatrix} 0 & 0 \end{bmatrix}

    D.

    [000]\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}

  3. 3.

    For a matrix A=[aij]4×3A = [a_{ij}]_{4 \times 3}, what is the maximum value of ii?

    A.

    3

    B.

    4

    C.

    12

    D.

    7

Download the worksheet for Matrices - Concept, notation, order, equality, types of matrices, zero and identity matrix to practice offline. It includes additional chapter-level practice questions.

Transpose of a matrix, symmetric and skew symmetric matrices

Subtopic

Transpose of a matrix, symmetric and skew symmetric matrices under Matrices for Grade 12 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If A=[1234]A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, then its transpose A′A' is:

    A.

    [1324]\begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix}

    B.

    [4321]\begin{bmatrix} 4 & 3 \\ 2 & 1 \end{bmatrix}

    C.

    [1234]\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}

    D.

    [2143]\begin{bmatrix} 2 & 1 \\ 4 & 3 \end{bmatrix}

  2. 2.

    For any square matrix AA, the matrix 12(A−A′)\frac{1}{2}(A - A') is always:

    A.

    Symmetric

    B.

    Skew-symmetric

    C.

    Identity

    D.

    Unitary

  3. 3.

    If A=[5665]A = \begin{bmatrix} 5 & 6 \\ 6 & 5 \end{bmatrix}, then A−A′A - A' is equal to:

    A.

    II

    B.

    2A2A

    C.

    [0000]\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}

    D.

    [10121210]\begin{bmatrix} 10 & 12 \\ 12 & 10 \end{bmatrix}

Download the worksheet for Matrices - Transpose of a matrix, symmetric and skew symmetric matrices to practice offline. It includes additional chapter-level practice questions.

Operation on matrices: Addition, multiplication and multiplication with a scalar

Subtopic

Operation on matrices: Addition, multiplication and multiplication with a scalar under Matrices for Grade 12 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If X+[1234]=[0000]X + \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} = \begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}, then XX is:

    A.

    [1234]\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}

    B.

    [−1−2−3−4]\begin{bmatrix} -1 & -2 \\ -3 & -4 \end{bmatrix}

    C.

    [0000]\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}

    D.

    [4321]\begin{bmatrix} 4 & 3 \\ 2 & 1 \end{bmatrix}

  2. 2.

    If A=[1201]A = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix} and B=[2002]B = \begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix}, then ABAB is:

    A.

    [2402]\begin{bmatrix} 2 & 4 \\ 0 & 2 \end{bmatrix}

    B.

    [2202]\begin{bmatrix} 2 & 2 \\ 0 & 2 \end{bmatrix}

    C.

    [3203]\begin{bmatrix} 3 & 2 \\ 0 & 3 \end{bmatrix}

    D.

    [2002]\begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix}

  3. 3.

    If A=[12]A = \begin{bmatrix} 1 \\ 2 \end{bmatrix} and B=[34]B = \begin{bmatrix} 3 & 4 \end{bmatrix}, the order of ABAB is:

    A.

    1×11 \times 1

    B.

    2×22 \times 2

    C.

    1×21 \times 2

    D.

    2×12 \times 1

Download the worksheet for Matrices - Operation on matrices: Addition, multiplication and multiplication with a scalar to practice offline. It includes additional chapter-level practice questions.

Simple properties of addition, multiplication and scalar multiplication

Subtopic

Simple properties of addition, multiplication and scalar multiplication under Matrices for Grade 12 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If A=[aij]A = [a_{ij}] is a square matrix such that aij=0a_{ij} = 0 for i≠ji \neq j, it is called a:

    A.

    Diagonal matrix

    B.

    Row matrix

    C.

    Column matrix

    D.

    Scalar matrix

  2. 2.

    A matrix having only one column is called a:

    A.

    Row matrix

    B.

    Column matrix

    C.

    Identity matrix

    D.

    Zero matrix

  3. 3.

    If A=[1234]A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, then A+AA + A is:

    A.

    [2468]\begin{bmatrix} 2 & 4 \\ 6 & 8 \end{bmatrix}

    B.

    [14916]\begin{bmatrix} 1 & 4 \\ 9 & 16 \end{bmatrix}

    C.

    [2234]\begin{bmatrix} 2 & 2 \\ 3 & 4 \end{bmatrix}

    D.

    [0000]\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}

Download the worksheet for Matrices - Simple properties of addition, multiplication and scalar multiplication to practice offline. It includes additional chapter-level practice questions.

Invertible matrices and proof of the uniqueness of inverse

Subtopic

Invertible matrices and proof of the uniqueness of inverse under Matrices for Grade 12 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    The uniqueness of the inverse theorem states that if a matrix has an inverse, it has:

    A.

    Exactly one inverse

    B.

    At least two inverses

    C.

    Infinite inverses

    D.

    No inverse

  2. 2.

    If a square matrix AA has an inverse BB, then the product of their determinants ∣A∣⋅∣B∣|A| \cdot |B| is:

    A.

    00

    B.

    11

    C.

    −1-1

    D.

    ∣A∣|A|

  3. 3.

    If AA is an invertible matrix and k=−1k = -1, then (−A)−1(-A)^{-1} is equal to:

    A.

    A−1A^{-1}

    B.

    −A−1-A^{-1}

    C.

    AA

    D.

    −A-A

Download the worksheet for Matrices - Invertible matrices and proof of the uniqueness of inverse to practice offline. It includes additional chapter-level practice questions.