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Indian Navy INET Matrices and Determinants — practice questions

Explore 31 free Matrices and Determinants questions in Indian Navy INET 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 1–30 of 31.

For 2×2 matrix A = [[2,3],[1,4]], A⁻¹ =Read the answer and worked solution →For matrices A, B (square, same size): (AB)^T =Read the answer and worked solution →A matrix is skew-symmetric if:Read the answer and worked solution →The transpose of $A^T$ is:Read the answer and worked solution →Match each kind of matrix to its conditionRead 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 →Complete the definition of a matrixRead 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 →Symmetric or skew symmetric?Read the answer and worked solution →True or false: matrix algebraRead the answer and worked solution →Complete the equality conditionRead 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 →Special square matricesRead the answer and worked solution →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 →Match each matrix termRead the answer and worked solution →

Worked practice questions

For 2×2 matrix A = [[2,3],[1,4]], A⁻¹ =

  1. [[1/2,1/3],[1,1/4]]
  2. I
  3. (1/|A|) × [[4,-3],[-1,2]] = (1/5)[[4,-3],[-1,2]]
  4. Same as A
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Correct answer: C. (1/|A|) × [[4,-3],[-1,2]] = (1/5)[[4,-3],[-1,2]]

|A| = 8 - 3 = 5. A⁻¹ = (1/|A|) × adj(A). For 2×2 [[a,b],[c,d]]: adj = [[d,-b],[-c,a]]. **So A⁻¹ = (1/5)[[4,-3],[-1,2]].**

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For matrices A, B (square, same size): (AB)^T =

  1. A^T × B^T
  2. A B
  3. (AB) directly
  4. B^T A^T (order reversed)
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Correct answer: D. B^T A^T (order reversed)

(AB)^T = B^T A^T. Important property: transpose reverses the order. Similarly (AB)⁻¹ = B⁻¹ A⁻¹.

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A matrix is skew-symmetric if:

  1. Diagonal nonzero
  2. A = 0
  3. A^T = -A (so a_(ii) = 0)
  4. A = A^T
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Correct answer: C. A^T = -A (so a_(ii) = 0)

**Skew-symmetric:** A^T = -A. Diagonal must be zero (since a_(ii) = -a_(ii)). 3D rotations have skew generators. Eigenvalues are pure imaginary (or zero).

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