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

12 questions · Seed 56 · 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 = [[9, 6], [2, 9]].
69
det(M) = (9 × 9) − (6 × 2) = 81 − 12 = 69.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 8], [8, 12]].
20
det(M) = (7 × 12) − (8 × 8) = 84 − 64 = 20.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [2, 4]].
24
det(M) = (7 × 4) − (2 × 2) = 28 − 4 = 24.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 9], [2, 7]].
-4
det(M) = (2 × 7) − (9 × 2) = 14 − 18 = -4.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [9, 7]].
5
det(M) = (11 × 7) − (8 × 9) = 77 − 72 = 5.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [4, 8]].
76
det(M) = (11 × 8) − (3 × 4) = 88 − 12 = 76.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [10, 3]].
1
det(M) = (7 × 3) − (2 × 10) = 21 − 20 = 1.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 3], [5, 7]].
34
det(M) = (7 × 7) − (3 × 5) = 49 − 15 = 34.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 8], [1, 2]].
8
det(M) = (8 × 2) − (8 × 1) = 16 − 8 = 8.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 8], [1, 11]].
124
det(M) = (12 × 11) − (8 × 1) = 132 − 8 = 124.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [2, 6]].
10
det(M) = (3 × 6) − (4 × 2) = 18 − 8 = 10.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 2], [2, 6]].
14
det(M) = (3 × 6) − (2 × 2) = 18 − 4 = 14.

12 questions · Seed 56 · 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 = [[9, 6], [2, 9]].
M = [ 9 6 ; 2 9 ] · det(M) = (9×9) − (6×2)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 8], [8, 12]].
M = [ 7 8 ; 8 12 ] · det(M) = (7×12) − (8×8)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [2, 4]].
M = [ 7 2 ; 2 4 ] · det(M) = (7×4) − (2×2)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 9], [2, 7]].
M = [ 2 9 ; 2 7 ] · det(M) = (2×7) − (9×2)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [9, 7]].
M = [ 11 8 ; 9 7 ] · det(M) = (11×7) − (8×9)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [4, 8]].
M = [ 11 3 ; 4 8 ] · det(M) = (11×8) − (3×4)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [10, 3]].
M = [ 7 2 ; 10 3 ] · det(M) = (7×3) − (2×10)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 3], [5, 7]].
M = [ 7 3 ; 5 7 ] · det(M) = (7×7) − (3×5)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 8], [1, 2]].
M = [ 8 8 ; 1 2 ] · det(M) = (8×2) − (8×1)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 8], [1, 11]].
M = [ 12 8 ; 1 11 ] · det(M) = (12×11) − (8×1)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [2, 6]].
M = [ 3 4 ; 2 6 ] · det(M) = (3×6) − (4×2)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 2], [2, 6]].
M = [ 3 2 ; 2 6 ] · det(M) = (3×6) − (2×2)

12 questions · Seed 56 · 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 = [[9, 6], [2, 9]].
69
det(M) = (9 × 9) − (6 × 2) = 81 − 12 = 69.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 8], [8, 12]].
20
det(M) = (7 × 12) − (8 × 8) = 84 − 64 = 20.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [2, 4]].
24
det(M) = (7 × 4) − (2 × 2) = 28 − 4 = 24.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 9], [2, 7]].
-4
det(M) = (2 × 7) − (9 × 2) = 14 − 18 = -4.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [9, 7]].
5
det(M) = (11 × 7) − (8 × 9) = 77 − 72 = 5.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [4, 8]].
76
det(M) = (11 × 8) − (3 × 4) = 88 − 12 = 76.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [10, 3]].
1
det(M) = (7 × 3) − (2 × 10) = 21 − 20 = 1.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 3], [5, 7]].
34
det(M) = (7 × 7) − (3 × 5) = 49 − 15 = 34.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 8], [1, 2]].
8
det(M) = (8 × 2) − (8 × 1) = 16 − 8 = 8.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 8], [1, 11]].
124
det(M) = (12 × 11) − (8 × 1) = 132 − 8 = 124.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [2, 6]].
10
det(M) = (3 × 6) − (4 × 2) = 18 − 8 = 10.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 2], [2, 6]].
14
det(M) = (3 × 6) − (2 × 2) = 18 − 4 = 14.

12 questions · Seed 56 · Age guidance, not curriculum certification