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 \( x \).