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Indian Navy 10+2 B.Tech Cadet Determinants — practice questions

Explore 27 free Determinants questions in Indian Navy 10+2 B.Tech Cadet 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 1–27 of 27.

For a square matrix $A$ of order $n$, the product $A\,(\text{adj}\,A)$ equals:Read the answer and worked solution →If $A$ is a $3\times3$ matrix with $|A| = 2$, then $|3A|$ equals:Read the answer and worked solution →Singular or non-singular?Read the answer and worked solution →Match each term to its definitionRead the answer and worked solution →Minors and cofactorsRead the answer and worked solution →True or false: cofactor expansionRead the answer and worked solution →Order the steps for finding A⁻¹Read the answer and worked solution →Determinant of a 2 × 2 matrixRead the answer and worked solution →Complete the inverse ruleRead the answer and worked solution →True or false: adjoint and inverseRead the answer and worked solution →Assertion and reason: invertibilityRead the answer and worked solution →Tap every statement that is true of a non-singular matrixRead the answer and worked solution →Spot the one that does not belongRead 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 →Flip and pair: symbol with meaningRead the answer and worked solution →Complete the area formulaRead the answer and worked solution →Adjoint and identityRead the answer and worked solution →Order the steps for the area of a triangleRead the answer and worked solution →Which side of the inverse test?Read the answer and worked solution →True or false: expanding a determinantRead the answer and worked solution →Match each condition to what it tells youRead the answer and worked solution →Assertion and reason: cofactorsRead the answer and worked solution →Spot the odd oneRead the answer and worked solution →Tap everything the chapter actually definesRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →Two true, one false: scope of the chapterRead the answer and worked solution →

Worked practice questions

For a square matrix $A$ of order $n$, the product $A\,(\text{adj}\,A)$ equals:

  1. $\text{adj}(A^2)$
  2. $I_n$
  3. $A^2$
  4. $|A|\,I_n$
Show answer and solution

Correct answer: D. $|A|\,I_n$

A·(adj A) = (adj A)·A = |A| Iₙ — the defining property used to derive A⁻¹ = adj A / |A|.

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If $A$ is a $3\times3$ matrix with $|A| = 2$, then $|3A|$ equals:

  1. 6
  2. 27
  3. 54
  4. 18
Show answer and solution

Correct answer: C. 54

|3A| = 3³|A| = 27·2 = 54 for a 3×3 matrix.

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Singular or non-singular?

Read exercise and reference answers
Items
  1. Item
    |A| = 0
    Category
    Singular
  2. Item
    |A| = −7
    Category
    Non-singular
  3. Item
    A has no inverse
    Category
    Singular
  4. Item
    A⁻¹ exists
    Category
    Non-singular
  5. Item
    |A| = 1
    Category
    Non-singular
  6. Item
    A(adj A) = O
    Category
    Singular
Categories
  1. Item
    Singular
  2. Item
    Non-singular
Your syllabus defines a square matrix as singular when |A| = 0 and non-singular when |A| ≠ 0. The whole inverse story hangs on which side a matrix falls. Source: syllabus Maths Part I, Ch 4 Determinants.

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