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Rajasthan Board Class 12 (RBSE) Matrices — practice questions

Explore 35 free Matrices questions in Rajasthan Board Class 12 (RBSE) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Matrices questions and exercises with answers

Showing questions 1–30 of 35.

The transpose of $A^T$ is:Read 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 →The transpose of the product (AB)^T equals:Read the answer and worked solution →Matrix multiplication is:Read the answer and worked solution →The determinant of the 2×2 matrix [[a, b], [c, d]] equals:Read the answer and worked solution →A matrix A has an INVERSE if and only if:Read the answer and worked solution →By Cramer's rule, the value of x_1 in Ax = b (where A is non-singular) is:Read the answer and worked solution →For the system Ax = b, if rank(A) < rank(augmented matrix A|b), the system has:Read the answer and worked solution →An ORTHOGONAL matrix A satisfies:Read the answer and worked solution →The CHARACTERISTIC EQUATION used to find eigenvalues of matrix A 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 →

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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For matrices A (3×2) and B (2×4), the product AB has order:

  1. $3 × 2$ (same as the order of matrix A)
  2. $2 × 4$ (same as the order of matrix B)
  3. $3 × 4$ (rows of A, cols of B)
  4. $2 × 2$ (taking smallest dimensions)
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Correct answer: C. $3 × 4$ (rows of A, cols of B)

AB exists if columns(A) = rows(B). Here 2 = 2 ✓. Result has order rows(A) × columns(B) = 3 × 4.

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The transpose of the product (AB)^T equals:

  1. $A^T B^T$ (same order)
  2. $B^T A^T$ (reversed order)
  3. $A B$ (no change)
  4. $(A B)^{-1}$ (the inverse instead)
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Correct answer: B. $B^T A^T$ (reversed order)

**Transpose reverses order in a product:** (AB)^T = B^T A^T. This is a fundamental matrix algebra rule. Similarly, (AB)^(-1) = B^(-1) A^(-1).

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