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JEE Advanced Determinants — practice questions — page 3

Explore 73 free Determinants questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Determinants questions and exercises with answers

Showing questions 61–73 of 73.

Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Tap every statement true of the identity matrixRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →True or false: inversesRead the answer and worked solution →Complete the scalar multiplication rulesRead the answer and worked solution →Which operation needs matching orders?Read the answer and worked solution →Spot the odd one outRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →Assertion and reason: structureRead the answer and worked solution →Order the steps: test whether A is symmetricRead the answer and worked solution →True or false: orders and shapesRead the answer and worked solution →

Worked practice questions

Assertion and reason

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Questions
  1. Reason
    A product needs the inner dimensions to agree, and swapping changes them.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    AB may exist while BA does not.
  2. Reason
    (AB)′ = B′A′.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    Transposing a product reverses the order of the factors.
  3. Reason
    Its diagonal entries are all equal to the constant 1.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    Every identity matrix is a scalar matrix.
  4. Reason
    A scalar matrix has equal diagonal entries.
    Verdict
    The assertion is false and the reason is true.
    Assertion
    Every scalar matrix is an identity matrix.
The reason must genuinely explain the assertion. Source: syllabus Maths Part I, Ch 3 Matrices.

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Two are true, one is not

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Questions
  1. False statement
    AB = BA for all matrices
    Statements
    1. A + B = B + A
    2. A(BC) = (AB)C
    3. AB = BA for all matrices
  2. False statement
    (AB)′ = A′B′
    Statements
    1. (AB)′ = A′B′
    2. (A′)′ = A
    3. (A + B)′ = A′ + B′
  3. False statement
    Every square matrix is symmetric
    Statements
    1. A symmetric matrix satisfies A′ = A
    2. Every square matrix is symmetric
    3. A skew symmetric matrix satisfies A′ = −A
The false line is always a rule of addition wrongly applied to multiplication. Source: syllabus Maths Part I, Ch 3 Matrices.

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Three of these are wrong. Find the one that holds.

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Questions
  1. Question
    Three of these statements about matrix products are false.
    Choices
    1. Item
      AB needs columns of A to match rows of B
      Correct
      Yes
    2. Explanation
      Matrix multiplication is not commutative.
      Item
      AB = BA always
    3. Explanation
      Their orders must still agree with each other.
      Item
      AB exists for any two square matrices
    4. Explanation
      It is rows of A by columns of B.
      Item
      AB has the order of A
  2. Question
    Three of these statements about inverses are false.
    Choices
    1. Item
      If AB = BA = I then B is the inverse of A
      Correct
      Yes
    2. Explanation
      Only some square matrices do.
      Item
      Every matrix has an inverse
    3. Explanation
      The inverse, when it exists, is unique.
      Item
      A matrix may have two different inverses
    4. Explanation
      The transpose is not generally the inverse.
      Item
      The inverse of A is A′
Each trap is a real one: commuting a product, or transposing without reversing. Source: syllabus Maths Part I, Ch 3 Matrices.

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