5.2 The identity matrix I Quiz: AQA Further Maths, Unit 5

The 20 questions

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

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

2. For any 2 x 2 matrix A, what is AI?

   • 2A
   • 0
   • A
   • I

3. Multiply [[3, 4], [5, 6]] by I. What is the result?

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

4. What effect does multiplying a matrix by the 2 × 2 identity matrix I have?

   • Rotation
   • No change
   • Doubles values
   • Reflection

5. What is I x I?

   • It is undefined
   • I
   • 2I
   • 0

6. What matrix leaves every 2 x 1 column vector unchanged when multiplied on the left?

   • [[2, 0], [0, 2]]
   • [[1, 1], [0, 0]]
   • I
   • [[0, 1], [1, 0]]

7. Which is the 2 x 2 zero matrix?

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

8. For which k is [[k, 0], [0, k]] equal to I?

   • 0
   • 2
   • -1
   • 1

9. Which property is demonstrated by the matrix equation M I = M?

   • Identity property
   • Associative property
   • Inverse property
   • Commutative property

10. If M x N = N for all 2 x 2 matrices N, what is M?

    • I
    • N
    • 0
    • 2I

11. What are the entries on the main diagonal of I?

    • All 2s
    • A 2 and a 0
    • All 0s
    • All 1s

12. The identity matrix acts on the point (3, -2) to give what?

    • (3, -2)
    • (-3, 2)
    • (0, 0)
    • (2, 3)

13. Find x and y if I x [[x], [y]] = [[5], [-1]].

    • x = 5, y = -1
    • x = -1, y = 5
    • x = 1, y = 5
    • x = 0, y = 0

14. For A = [[2, 1], [1, 2]], what is A - 2I?

    • [[0, 1], [1, 0]]
    • [[0, -1], [-1, 0]]
    • [[2, 1], [1, 2]]
    • [[1, 1], [1, 1]]

15. For A = [[3, 0], [0, 3]], find k so that A - kI is the zero matrix.

    • 6
    • -3
    • 0
    • 3

16. Which 2 x 2 matrix leaves the unit square unchanged?

    • A rotation of 90 degrees
    • [[2, 0], [0, 2]]
    • The zero matrix
    • I

17. Which matrix is I + [[0, 1], [0, 0]]?

    • [[2, 1], [0, 2]]
    • [[1, 1], [0, 1]]
    • [[1, 0], [1, 1]]
    • [[0, 1], [0, 0]]

18. Let E = [[0, 1], [0, 0]]. What is (I + E) x (I + E)?

    • [[1, 1], [0, 1]]
    • [[1, 2], [0, 1]]
    • [[1, 0], [0, 1]]
    • [[2, 2], [0, 2]]

19. What is the result of multiplying any 2 × 2 matrix M by the identity matrix I?

    • Matrix M
    • The zero matrix
    • Matrix -M
    • The identity matrix

20. What is I^5?

    • I
    • 5I
    • [[5, 0], [0, 5]]
    • 0

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