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

12 questions · Seed 60 · 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, 9], [9, 4]].
-49
det(M) = (8 × 4) − (9 × 9) = 32 − 81 = -49.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [10, 6]].
-50
det(M) = (5 × 6) − (8 × 10) = 30 − 80 = -50.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 7], [6, 2]].
-30
det(M) = (6 × 2) − (7 × 6) = 12 − 42 = -30.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 7], [8, 5]].
-31
det(M) = (5 × 5) − (7 × 8) = 25 − 56 = -31.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [3, 3]].
6
det(M) = (10 × 3) − (8 × 3) = 30 − 24 = 6.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 10], [6, 6]].
-42
det(M) = (3 × 6) − (10 × 6) = 18 − 60 = -42.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [6, 11]].
103
det(M) = (11 × 11) − (3 × 6) = 121 − 18 = 103.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 4], [7, 7]].
28
det(M) = (8 × 7) − (4 × 7) = 56 − 28 = 28.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 9], [5, 7]].
25
det(M) = (10 × 7) − (9 × 5) = 70 − 45 = 25.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [8, 10]].
54
det(M) = (7 × 10) − (2 × 8) = 70 − 16 = 54.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [9, 8]].
-21
det(M) = (3 × 8) − (5 × 9) = 24 − 45 = -21.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 5], [9, 5]].
-35
det(M) = (2 × 5) − (5 × 9) = 10 − 45 = -35.

12 questions · Seed 60 · 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, 9], [9, 4]].
M = [ 8 9 ; 9 4 ] · det(M) = (8×4) − (9×9)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [10, 6]].
M = [ 5 8 ; 10 6 ] · det(M) = (5×6) − (8×10)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 7], [6, 2]].
M = [ 6 7 ; 6 2 ] · det(M) = (6×2) − (7×6)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 7], [8, 5]].
M = [ 5 7 ; 8 5 ] · det(M) = (5×5) − (7×8)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [3, 3]].
M = [ 10 8 ; 3 3 ] · det(M) = (10×3) − (8×3)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 10], [6, 6]].
M = [ 3 10 ; 6 6 ] · det(M) = (3×6) − (10×6)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [6, 11]].
M = [ 11 3 ; 6 11 ] · det(M) = (11×11) − (3×6)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 4], [7, 7]].
M = [ 8 4 ; 7 7 ] · det(M) = (8×7) − (4×7)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 9], [5, 7]].
M = [ 10 9 ; 5 7 ] · det(M) = (10×7) − (9×5)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [8, 10]].
M = [ 7 2 ; 8 10 ] · det(M) = (7×10) − (2×8)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [9, 8]].
M = [ 3 5 ; 9 8 ] · det(M) = (3×8) − (5×9)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 5], [9, 5]].
M = [ 2 5 ; 9 5 ] · det(M) = (2×5) − (5×9)

12 questions · Seed 60 · 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, 9], [9, 4]].
-49
det(M) = (8 × 4) − (9 × 9) = 32 − 81 = -49.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [10, 6]].
-50
det(M) = (5 × 6) − (8 × 10) = 30 − 80 = -50.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 7], [6, 2]].
-30
det(M) = (6 × 2) − (7 × 6) = 12 − 42 = -30.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 7], [8, 5]].
-31
det(M) = (5 × 5) − (7 × 8) = 25 − 56 = -31.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [3, 3]].
6
det(M) = (10 × 3) − (8 × 3) = 30 − 24 = 6.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 10], [6, 6]].
-42
det(M) = (3 × 6) − (10 × 6) = 18 − 60 = -42.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [6, 11]].
103
det(M) = (11 × 11) − (3 × 6) = 121 − 18 = 103.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 4], [7, 7]].
28
det(M) = (8 × 7) − (4 × 7) = 56 − 28 = 28.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 9], [5, 7]].
25
det(M) = (10 × 7) − (9 × 5) = 70 − 45 = 25.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [8, 10]].
54
det(M) = (7 × 10) − (2 × 8) = 70 − 16 = 54.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [9, 8]].
-21
det(M) = (3 × 8) − (5 × 9) = 24 − 45 = -21.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 5], [9, 5]].
-35
det(M) = (2 × 5) − (5 × 9) = 10 − 45 = -35.

12 questions · Seed 60 · Age guidance, not curriculum certification