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

12 questions · Seed 104747 · 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, 7], [8, 9]].
-2
det(M) = (6 × 9) − (7 × 8) = 54 − 56 = -2.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 9], [10, 9]].
18
det(M) = (12 × 9) − (9 × 10) = 108 − 90 = 18.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 10], [10, 6]].
-46
det(M) = (9 × 6) − (10 × 10) = 54 − 100 = -46.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 7], [7, 12]].
95
det(M) = (12 × 12) − (7 × 7) = 144 − 49 = 95.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [1, 6]].
47
det(M) = (8 × 6) − (1 × 1) = 48 − 1 = 47.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 8], [7, 2]].
-42
det(M) = (7 × 2) − (8 × 7) = 14 − 56 = -42.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [7, 3]].
-22
det(M) = (2 × 3) − (4 × 7) = 6 − 28 = -22.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 8], [3, 9]].
39
det(M) = (7 × 9) − (8 × 3) = 63 − 24 = 39.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [3, 3]].
15
det(M) = (8 × 3) − (3 × 3) = 24 − 9 = 15.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 4], [1, 2]].
18
det(M) = (11 × 2) − (4 × 1) = 22 − 4 = 18.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [3, 3]].
6
det(M) = (12 × 3) − (10 × 3) = 36 − 30 = 6.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 7], [6, 10]].
38
det(M) = (8 × 10) − (7 × 6) = 80 − 42 = 38.

12 questions · Seed 104747 · 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, 7], [8, 9]].
M = [ 6 7 ; 8 9 ] · det(M) = (6×9) − (7×8)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 9], [10, 9]].
M = [ 12 9 ; 10 9 ] · det(M) = (12×9) − (9×10)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 10], [10, 6]].
M = [ 9 10 ; 10 6 ] · det(M) = (9×6) − (10×10)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 7], [7, 12]].
M = [ 12 7 ; 7 12 ] · det(M) = (12×12) − (7×7)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [1, 6]].
M = [ 8 1 ; 1 6 ] · det(M) = (8×6) − (1×1)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 8], [7, 2]].
M = [ 7 8 ; 7 2 ] · det(M) = (7×2) − (8×7)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [7, 3]].
M = [ 2 4 ; 7 3 ] · det(M) = (2×3) − (4×7)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 8], [3, 9]].
M = [ 7 8 ; 3 9 ] · det(M) = (7×9) − (8×3)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [3, 3]].
M = [ 8 3 ; 3 3 ] · det(M) = (8×3) − (3×3)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 4], [1, 2]].
M = [ 11 4 ; 1 2 ] · det(M) = (11×2) − (4×1)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [3, 3]].
M = [ 12 10 ; 3 3 ] · det(M) = (12×3) − (10×3)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 7], [6, 10]].
M = [ 8 7 ; 6 10 ] · det(M) = (8×10) − (7×6)

12 questions · Seed 104747 · 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, 7], [8, 9]].
-2
det(M) = (6 × 9) − (7 × 8) = 54 − 56 = -2.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 9], [10, 9]].
18
det(M) = (12 × 9) − (9 × 10) = 108 − 90 = 18.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 10], [10, 6]].
-46
det(M) = (9 × 6) − (10 × 10) = 54 − 100 = -46.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 7], [7, 12]].
95
det(M) = (12 × 12) − (7 × 7) = 144 − 49 = 95.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [1, 6]].
47
det(M) = (8 × 6) − (1 × 1) = 48 − 1 = 47.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 8], [7, 2]].
-42
det(M) = (7 × 2) − (8 × 7) = 14 − 56 = -42.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [7, 3]].
-22
det(M) = (2 × 3) − (4 × 7) = 6 − 28 = -22.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 8], [3, 9]].
39
det(M) = (7 × 9) − (8 × 3) = 63 − 24 = 39.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [3, 3]].
15
det(M) = (8 × 3) − (3 × 3) = 24 − 9 = 15.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 4], [1, 2]].
18
det(M) = (11 × 2) − (4 × 1) = 22 − 4 = 18.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [3, 3]].
6
det(M) = (12 × 3) − (10 × 3) = 36 − 30 = 6.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 7], [6, 10]].
38
det(M) = (8 × 10) − (7 × 6) = 80 − 42 = 38.

12 questions · Seed 104747 · Age guidance, not curriculum certification