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

Explore 28 free Matrices and 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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Matrices and Determinants questions and exercises with answers

Showing questions 1–28 of 28.

If A is orthogonal (A A^T = I), then |A| =Read the answer and worked solution →Trace of matrix is sum of diagonal entries. For 2×2 [[a,b],[c,d]]: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 →

Worked practice questions

If A is orthogonal (A A^T = I), then |A| =

  1. |A|²
  2. 2
  3. ±1
  4. 0
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Correct answer: C. ±1

|A A^T| = |I| = 1. But |A A^T| = |A| × |A^T| = |A|². So |A|² = 1 → |A| = ±1. Det +1: proper rotation. **Det -1:** improper (rotation × reflection).

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Trace of matrix is sum of diagonal entries. For 2×2 [[a,b],[c,d]]:

  1. det = ad - bc
  2. a + b + c + d
  3. a + d (= sum of eigenvalues)
  4. a × d
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Correct answer: C. a + d (= sum of eigenvalues)

Trace = sum of diagonal = a + d. Equals sum of eigenvalues. **Cyclic invariance:** tr(AB) = tr(BA). Trace is basis-independent.

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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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