MathsAges 16-18

2×2 matrix determinants

Evaluate the determinant det(M) = ad − bc of a 2 × 2 matrix from its leading and secondary diagonals. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

2×2 matrix determinants

Take your time. Show your thinking.

1. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 4], [7, 6]].
M = [ 6 4 ; 7 6 ] · det(M) = (6×6) − (4×7)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 1], [4, 10]].
M = [ 9 1 ; 4 10 ] · det(M) = (9×10) − (1×4)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 8], [4, 5]].
M = [ 12 8 ; 4 5 ] · det(M) = (12×5) − (8×4)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [1, 6]].
M = [ 6 1 ; 1 6 ] · det(M) = (6×6) − (1×1)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 1], [6, 12]].
M = [ 10 1 ; 6 12 ] · det(M) = (10×12) − (1×6)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 4], [10, 5]].
M = [ 4 4 ; 10 5 ] · det(M) = (4×5) − (4×10)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 3], [1, 12]].
M = [ 9 3 ; 1 12 ] · det(M) = (9×12) − (3×1)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [1, 6]].
M = [ 4 6 ; 1 6 ] · det(M) = (4×6) − (6×1)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 1], [6, 11]].
M = [ 11 1 ; 6 11 ] · det(M) = (11×11) − (1×6)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 1], [3, 6]].
M = [ 10 1 ; 3 6 ] · det(M) = (10×6) − (1×3)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [5, 10]].
M = [ 5 1 ; 5 10 ] · det(M) = (5×10) − (1×5)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [5, 7]].
M = [ 6 10 ; 5 7 ] · det(M) = (6×7) − (10×5)

12 questions · Seed 48 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

2×2 matrix determinants

Answers and reasoning. Review before teaching.

1. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 4], [7, 6]].
8
det(M) = (6 × 6) − (4 × 7) = 36 − 28 = 8.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 1], [4, 10]].
86
det(M) = (9 × 10) − (1 × 4) = 90 − 4 = 86.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 8], [4, 5]].
28
det(M) = (12 × 5) − (8 × 4) = 60 − 32 = 28.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [1, 6]].
35
det(M) = (6 × 6) − (1 × 1) = 36 − 1 = 35.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 1], [6, 12]].
114
det(M) = (10 × 12) − (1 × 6) = 120 − 6 = 114.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 4], [10, 5]].
-20
det(M) = (4 × 5) − (4 × 10) = 20 − 40 = -20.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 3], [1, 12]].
105
det(M) = (9 × 12) − (3 × 1) = 108 − 3 = 105.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [1, 6]].
18
det(M) = (4 × 6) − (6 × 1) = 24 − 6 = 18.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 1], [6, 11]].
115
det(M) = (11 × 11) − (1 × 6) = 121 − 6 = 115.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 1], [3, 6]].
57
det(M) = (10 × 6) − (1 × 3) = 60 − 3 = 57.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [5, 10]].
45
det(M) = (5 × 10) − (1 × 5) = 50 − 5 = 45.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [5, 7]].
-8
det(M) = (6 × 7) − (10 × 5) = 42 − 50 = -8.

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

2×2 matrix determinants

Take your time. Show your thinking.

1. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 4], [7, 6]].
M = [ 6 4 ; 7 6 ] · det(M) = (6×6) − (4×7)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 1], [4, 10]].
M = [ 9 1 ; 4 10 ] · det(M) = (9×10) − (1×4)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 8], [4, 5]].
M = [ 12 8 ; 4 5 ] · det(M) = (12×5) − (8×4)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [1, 6]].
M = [ 6 1 ; 1 6 ] · det(M) = (6×6) − (1×1)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 1], [6, 12]].
M = [ 10 1 ; 6 12 ] · det(M) = (10×12) − (1×6)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 4], [10, 5]].
M = [ 4 4 ; 10 5 ] · det(M) = (4×5) − (4×10)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 3], [1, 12]].
M = [ 9 3 ; 1 12 ] · det(M) = (9×12) − (3×1)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [1, 6]].
M = [ 4 6 ; 1 6 ] · det(M) = (4×6) − (6×1)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 1], [6, 11]].
M = [ 11 1 ; 6 11 ] · det(M) = (11×11) − (1×6)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 1], [3, 6]].
M = [ 10 1 ; 3 6 ] · det(M) = (10×6) − (1×3)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [5, 10]].
M = [ 5 1 ; 5 10 ] · det(M) = (5×10) − (1×5)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [5, 7]].
M = [ 6 10 ; 5 7 ] · det(M) = (6×7) − (10×5)

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

2×2 matrix determinants

Answers and reasoning. Review before teaching.

1. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 4], [7, 6]].
8
det(M) = (6 × 6) − (4 × 7) = 36 − 28 = 8.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 1], [4, 10]].
86
det(M) = (9 × 10) − (1 × 4) = 90 − 4 = 86.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 8], [4, 5]].
28
det(M) = (12 × 5) − (8 × 4) = 60 − 32 = 28.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [1, 6]].
35
det(M) = (6 × 6) − (1 × 1) = 36 − 1 = 35.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 1], [6, 12]].
114
det(M) = (10 × 12) − (1 × 6) = 120 − 6 = 114.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 4], [10, 5]].
-20
det(M) = (4 × 5) − (4 × 10) = 20 − 40 = -20.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 3], [1, 12]].
105
det(M) = (9 × 12) − (3 × 1) = 108 − 3 = 105.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [1, 6]].
18
det(M) = (4 × 6) − (6 × 1) = 24 − 6 = 18.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 1], [6, 11]].
115
det(M) = (11 × 11) − (1 × 6) = 121 − 6 = 115.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 1], [3, 6]].
57
det(M) = (10 × 6) − (1 × 3) = 60 − 3 = 57.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [5, 10]].
45
det(M) = (5 × 10) − (1 × 5) = 50 − 5 = 45.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [5, 7]].
-8
det(M) = (6 × 7) − (10 × 5) = 42 − 50 = -8.

12 questions · Seed 48 · Age guidance, not curriculum certification