Class 12 Matrices Practice Worksheet (CBSE & ISC 2025 Edition)

Class 12 Maths – Matrices Worksheet | CBSE & ISC Board Practice 2025

Class 12 – Matrices Practice Worksheet (With HOTS & Exam-Based Questions)

Class 12 – Matrices Practice Worksheet

Designed for: CBSE & ISC Mathematics (2025 Syllabus)
Topic: Matrices | Total Questions: 16 | Coverage: 1-mark to HOTS

🔹 Section A – Very Short Answer Questions (1 Mark Each)

  • 1. Define a diagonal matrix with an example.
  • 2. Find the transpose of \( A = [[2, 3], [0, 4]] \).
  • 3. Find the order of a matrix having 3 rows and 5 columns.
  • 4. Write the additive identity for matrix addition.
  • 5. If \( A + B \) is defined, what must be true about the order of A and B?

🔹 Section B – Short Answer Questions (2 Marks Each)

Attempt any three:

  • 6. Find \( A + B \) for \( A = [[1,2],[3,4]], B = [[4,3],[2,1]] \).
  • 7. Verify if matrix multiplication is commutative for \( A = I_2, B = [[2,3],[4,5]] \).
  • 8. Show that \( A^2 = -I \) for \( A = [[0,1],[-1,0]] \).

🔹 Section C – Application/Problem Solving (3 Marks Each)

Attempt any three:

  • 9. Show that \( A + A^T \) is symmetric for \( A = [[a,b],[c,d]] \).
  • 10. Find \( AB \) and \( BA \) for the given matrices. Check if \( AB = BA \).
  • 11. Multiply \( A = [[1,2,3],[4,5,6]] \) and \( B = [[7,8],[9,10],[11,12]] \).

🔹 Section D – Long Answer Questions (4 Marks Each)

Attempt any two:

  • 12. Prove that \( (A + A^T)^T = A + A^T \) for \( A = [[1,2],[3,4]] \).
  • 13. Find \( A^3 \) where \( A = [[1,2],[0,1]] \).
  • 14. For \( A = [[1,0],[2,1]] \), prove a general formula for \( A^n \) by induction.

🔹 Section E – HOTS (Higher Order Thinking Skills) (4 Marks Each)

Attempt both:

  • 15. If \( A^2 – 5A + 6I = 0 \), find \( A^{-1} \).
  • 16. For \( A = [[x,2],[-2,x]] \) and \( A^2 = I \), find all possible values of \( x \).

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