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Indian Navy AA (Artificer Apprentice) Matrices and Determinants — practice questions

Explore 31 free Matrices and Determinants questions in Indian Navy AA (Artificer Apprentice) 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 matrix multiplication AB to be defined:Read the answer and worked solution →Determinant of triangular (upper or lower) matrix:Read the answer and worked solution →A matrix is invertible iff:Read the answer and worked solution →A matrix is skew-symmetric if: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 matrix multiplication AB to be defined:

  1. Both must be square
  2. A and B must be same size
  3. Number of columns of A must equal number of rows of B
  4. Both must be 2×2
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Correct answer: C. Number of columns of A must equal number of rows of B

AB defined when columns of A = rows of B. If A is m×p and B is p×n, then AB is m×n. Otherwise undefined.

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Determinant of triangular (upper or lower) matrix:

  1. Always 1
  2. Product of diagonal entries
  3. Sum of entries
  4. Always 0
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Correct answer: B. Product of diagonal entries

For triangular matrix, det = product of diagonal entries. Includes diagonal matrices. Why row reduction to triangular form is useful for computing determinants.

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A matrix is invertible iff:

  1. Symmetric
  2. Its determinant is non-zero
  3. All entries are non-zero
  4. It is square
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Correct answer: B. Its determinant is non-zero

Square matrix A invertible (i.e., has A⁻¹ with AA⁻¹ = I) iff |A| ≠ 0. Equivalently: rows (and columns) are linearly independent.

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