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JEE Main Matrices and Determinants — practice questions — page 2

Explore 89 free Matrices and Determinants questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Matrices and Determinants questions and exercises with answers

Showing questions 31–60 of 89.

The transpose of $A^T$ is:Read the answer and worked solution →Tap every statement true of the identity matrixRead the answer and worked solution →A matrix A has an INVERSE if and only if:Read the answer and worked solution →Special square matricesRead the answer and worked solution →Order the steps: is AB defined, and what order is it?Read the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Assertion and reason: structureRead the answer and worked solution →True or false: orders and shapesRead the answer and worked solution →Matrix multiplication is:Read the answer and worked solution →The CHARACTERISTIC EQUATION used to find eigenvalues of matrix A is:Read the answer and worked solution →Sort each matrix by its shapeRead the answer and worked solution →Tap every matrix that must be squareRead the answer and worked solution →When is a product defined?Read the answer and worked solution →True or false: transposesRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →True or false: inversesRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →An ORTHOGONAL matrix A satisfies:Read the answer and worked solution →Which operation needs matching orders?Read the answer and worked solution →The determinant of the 2×2 matrix [[a, b], [c, d]] equals:Read the answer and worked solution →Complete the definition of a matrixRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →True or false: matrix algebraRead the answer and worked solution →For matrices A (3×2) and B (2×4), the product AB has order:Read the answer and worked solution →Two true, one false: scope of the chapterRead the answer and worked solution →Assertion and reason: invertibilityRead the answer and worked solution →True or false: cofactor expansionRead the answer and worked solution →Minors and cofactorsRead the answer and worked solution →Order the steps for finding A⁻¹Read the answer and worked solution →Complete the inverse ruleRead the answer and worked solution →

Worked practice questions

The transpose of $A^T$ is:

  1. $A$, since transposing twice returns the original on chart
  2. $A^{-1}$, the inverse of the matrix on the school chart
  3. $-A$, the negative of the original matrix here always
  4. $2A$, twice the matrix value on the school chart here
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Correct answer: A. $A$, since transposing twice returns the original on chart

$(A^T)^T = A$, transposing twice returns the original.

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Tap every statement true of the identity matrix

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Questions
  1. Items
    1. Text
      Diagonal entries are all 1
      Matches the category
      Yes
    2. Text
      Off-diagonal entries are all 0
      Matches the category
      Yes
    3. Text
      It is a square matrix
      Matches the category
      Yes
    4. Text
      All its entries are 1
      Matches the category
      No
    5. Text
      It is the zero matrix
      Matches the category
      No
    Category
    True of the identity matrix I
The identity is the multiplicative anchor of the whole chapter. Source: syllabus Maths Part I, Ch 3 Matrices.

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A matrix A has an INVERSE if and only if:

  1. $\det(A) \neq 0$ (non-singular matrix)
  2. $\det(A) = 0$ (singular matrix)
  3. $A$ is square (regardless of det)
  4. $A$ is symmetric only
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Correct answer: A. $\det(A) \neq 0$ (non-singular matrix)

Inverse A^(-1) exists ⇔ A is square AND non-singular (det A ≠ 0). **Formula:** A^(-1) = adj(A) / det(A). Singular matrices (det = 0) cannot be inverted.

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