C1-C2 Matrix operations, zero and identity matrices Quiz: AQA Further Maths, Unit 2

The 20 questions

1. What is the 2 x 2 identity matrix I?

   • [[1, 1], [1, 1]]
   • [[1, 0], [0, 1]]
   • [[0, 0], [0, 0]]
   • [[0, 1], [1, 0]]

2. Which matrix is the 2 x 2 zero matrix?

   • [[0, 0], [0, 0]]
   • [[1, 1], [1, 1]]
   • [[1, 0], [0, 1]]
   • [[0, 1], [0, 0]]

3. If matrix A has order 2 × 3 and matrix B has order 2 × 2, what is AB?

   • Order 2 × 2
   • Order 3 × 2
   • Order 2 × 3
   • Not defined

4. What is the order of the product of a 2 x 3 matrix and a 3 x 4 matrix?

   • 3 x 3
   • 2 x 4
   • 4 x 2
   • 2 x 3

5. For A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], what is AB?

   • [[2, 4], [1, 3]]
   • [[3, 4], [1, 2]]
   • [[2, 1], [4, 3]]
   • [[1, 2], [3, 4]]

6. For A = [[1, 0], [2, 1]] and B = [[1, 1], [0, 2]], what is 2A - 3B?

   • [[-1, -3], [4, -4]]
   • [[-1, -3], [4, 4]]
   • [[-1, 3], [4, -4]]
   • [[1, -3], [4, 4]]

7. What is A^2 for A = [[2, 1], [0, 3]]?

   • [[5, 4], [0, 9]]
   • [[4, 3], [0, 9]]
   • [[4, 5], [0, 9]]
   • [[4, 2], [0, 6]]

8. What is (3I)A for A = [[1, 2], [0, 4]]?

   • [[3, 6], [0, 12]]
   • [[3, 2], [0, 4]]
   • [[3, 6], [0, 4]]
   • [[4, 8], [0, 16]]

9. If A = [[1, 1], [1, 1]] and B = [[1, -1], [-1, 1]], what is the product AB?

   • Identity matrix
   • Matrix B
   • Zero matrix
   • Matrix A

10. For any 2 × 2 matrix A and identity matrix I, what does AI equal?

    • I
    • A²
    • Zero matrix
    • A

11. For what real x does [[x, 1], [1, x]] times [[1], [1]] equal [[3], [3]]?

    • x = 2
    • x = 4
    • x = 1
    • x = 3

12. Find X satisfying 2X + I = [[3, 4], [5, 6]].

    • [[1, 2], [2, 2]]
    • [[1, 2], [2.5, 2.5]]
    • [[1.5, 2], [2.5, 3]]
    • [[2, 4], [5, 5]]

13. For A = [[0, 1], [0, 0]], what is A^2?

    • A itself
    • The identity matrix
    • The zero matrix
    • [[0, 2], [0, 0]]

14. For M = [[1, k], [0, 1]], what is M^3?

    • [[1, 3k], [0, 1]]
    • [[1, k^3], [0, 1]]
    • [[3, 3k], [0, 3]]
    • [[1, 2k], [0, 1]]

15. If matrix A is 3 × 2 and matrix B is 2 × 4, what is the order of AB?

    • 4 × 3
    • 2 × 2
    • Not defined
    • 3 × 4

16. What is 4 times the matrix [[1, -1], [2, 0]]?

    • [[4, -4], [8, 0]]
    • [[4, -1], [2, 0]]
    • [[5, 3], [6, 4]]
    • [[4, -4], [2, 0]]

17. What is the product AB for A = [[1, 2], [0, 1]] and B = [[1, 0], [3, 1]]?

    • [[1, 2], [3, 1]]
    • [[7, 2], [3, 1]]
    • [[7, 3], [2, 1]]
    • [[7, 2], [0, 1]]

18. Which matrix is 2I - [[1, 0], [0, 3]]?

    • [[3, 0], [0, 5]]
    • [[1, 0], [0, 1]]
    • [[1, 0], [0, 5]]
    • [[1, 0], [0, -1]]

19. Solve [[1, 2], [0, 1]] times [[x], [y]] equals [[5], [2]].

    • x = 3, y = 1
    • x = 2, y = 1
    • x = 1, y = 2
    • x = 5, y = 2

20. What is the product of any 2x2 matrix and the 2x2 zero matrix?

    • The zero matrix
    • A non-zero matrix
    • The inverse matrix
    • The identity matrix

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