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

12 questions · Seed 104731 · 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 = [[8, 4], [6, 11]].
64
det(M) = (8 × 11) − (4 × 6) = 88 − 24 = 64.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 1], [5, 6]].
61
det(M) = (11 × 6) − (1 × 5) = 66 − 5 = 61.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 4], [9, 7]].
41
det(M) = (11 × 7) − (4 × 9) = 77 − 36 = 41.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [1, 5]].
50
det(M) = (12 × 5) − (10 × 1) = 60 − 10 = 50.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 10], [4, 9]].
32
det(M) = (8 × 9) − (10 × 4) = 72 − 40 = 32.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [5, 9]].
7
det(M) = (3 × 9) − (4 × 5) = 27 − 20 = 7.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 10], [10, 4]].
-60
det(M) = (10 × 4) − (10 × 10) = 40 − 100 = -60.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [9, 8]].
-22
det(M) = (4 × 8) − (6 × 9) = 32 − 54 = -22.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 5], [1, 6]].
7
det(M) = (2 × 6) − (5 × 1) = 12 − 5 = 7.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [9, 6]].
39
det(M) = (8 × 6) − (1 × 9) = 48 − 9 = 39.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 7], [8, 10]].
-26
det(M) = (3 × 10) − (7 × 8) = 30 − 56 = -26.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [10, 3]].
-34
det(M) = (2 × 3) − (4 × 10) = 6 − 40 = -34.

12 questions · Seed 104731 · 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 = [[8, 4], [6, 11]].
M = [ 8 4 ; 6 11 ] · det(M) = (8×11) − (4×6)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 1], [5, 6]].
M = [ 11 1 ; 5 6 ] · det(M) = (11×6) − (1×5)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 4], [9, 7]].
M = [ 11 4 ; 9 7 ] · det(M) = (11×7) − (4×9)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [1, 5]].
M = [ 12 10 ; 1 5 ] · det(M) = (12×5) − (10×1)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 10], [4, 9]].
M = [ 8 10 ; 4 9 ] · det(M) = (8×9) − (10×4)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [5, 9]].
M = [ 3 4 ; 5 9 ] · det(M) = (3×9) − (4×5)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 10], [10, 4]].
M = [ 10 10 ; 10 4 ] · det(M) = (10×4) − (10×10)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [9, 8]].
M = [ 4 6 ; 9 8 ] · det(M) = (4×8) − (6×9)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 5], [1, 6]].
M = [ 2 5 ; 1 6 ] · det(M) = (2×6) − (5×1)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [9, 6]].
M = [ 8 1 ; 9 6 ] · det(M) = (8×6) − (1×9)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 7], [8, 10]].
M = [ 3 7 ; 8 10 ] · det(M) = (3×10) − (7×8)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [10, 3]].
M = [ 2 4 ; 10 3 ] · det(M) = (2×3) − (4×10)

12 questions · Seed 104731 · 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 = [[8, 4], [6, 11]].
64
det(M) = (8 × 11) − (4 × 6) = 88 − 24 = 64.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 1], [5, 6]].
61
det(M) = (11 × 6) − (1 × 5) = 66 − 5 = 61.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 4], [9, 7]].
41
det(M) = (11 × 7) − (4 × 9) = 77 − 36 = 41.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [1, 5]].
50
det(M) = (12 × 5) − (10 × 1) = 60 − 10 = 50.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 10], [4, 9]].
32
det(M) = (8 × 9) − (10 × 4) = 72 − 40 = 32.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [5, 9]].
7
det(M) = (3 × 9) − (4 × 5) = 27 − 20 = 7.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 10], [10, 4]].
-60
det(M) = (10 × 4) − (10 × 10) = 40 − 100 = -60.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 6], [9, 8]].
-22
det(M) = (4 × 8) − (6 × 9) = 32 − 54 = -22.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 5], [1, 6]].
7
det(M) = (2 × 6) − (5 × 1) = 12 − 5 = 7.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [9, 6]].
39
det(M) = (8 × 6) − (1 × 9) = 48 − 9 = 39.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 7], [8, 10]].
-26
det(M) = (3 × 10) − (7 × 8) = 30 − 56 = -26.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [10, 3]].
-34
det(M) = (2 × 3) − (4 × 10) = 6 − 40 = -34.

12 questions · Seed 104731 · Age guidance, not curriculum certification