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

12 questions · Seed 51 · 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 = [[3, 9], [1, 12]].
27
det(M) = (3 × 12) − (9 × 1) = 36 − 9 = 27.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [5, 4]].
17
det(M) = (8 × 4) − (3 × 5) = 32 − 15 = 17.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 1], [4, 9]].
104
det(M) = (12 × 9) − (1 × 4) = 108 − 4 = 104.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 2], [4, 4]].
4
det(M) = (3 × 4) − (2 × 4) = 12 − 8 = 4.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [4, 12]].
36
det(M) = (6 × 12) − (9 × 4) = 72 − 36 = 36.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [7, 9]].
-16
det(M) = (6 × 9) − (10 × 7) = 54 − 70 = -16.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 9], [6, 7]].
9
det(M) = (9 × 7) − (9 × 6) = 63 − 54 = 9.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [10, 3]].
-49
det(M) = (7 × 3) − (7 × 10) = 21 − 70 = -49.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 7], [7, 9]].
59
det(M) = (12 × 9) − (7 × 7) = 108 − 49 = 59.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 1], [7, 11]].
125
det(M) = (12 × 11) − (1 × 7) = 132 − 7 = 125.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [5, 3]].
-1
det(M) = (8 × 3) − (5 × 5) = 24 − 25 = -1.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 7], [8, 6]].
-8
det(M) = (8 × 6) − (7 × 8) = 48 − 56 = -8.

12 questions · Seed 51 · 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 = [[3, 9], [1, 12]].
M = [ 3 9 ; 1 12 ] · det(M) = (3×12) − (9×1)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [5, 4]].
M = [ 8 3 ; 5 4 ] · det(M) = (8×4) − (3×5)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 1], [4, 9]].
M = [ 12 1 ; 4 9 ] · det(M) = (12×9) − (1×4)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 2], [4, 4]].
M = [ 3 2 ; 4 4 ] · det(M) = (3×4) − (2×4)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [4, 12]].
M = [ 6 9 ; 4 12 ] · det(M) = (6×12) − (9×4)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [7, 9]].
M = [ 6 10 ; 7 9 ] · det(M) = (6×9) − (10×7)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 9], [6, 7]].
M = [ 9 9 ; 6 7 ] · det(M) = (9×7) − (9×6)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [10, 3]].
M = [ 7 7 ; 10 3 ] · det(M) = (7×3) − (7×10)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 7], [7, 9]].
M = [ 12 7 ; 7 9 ] · det(M) = (12×9) − (7×7)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 1], [7, 11]].
M = [ 12 1 ; 7 11 ] · det(M) = (12×11) − (1×7)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [5, 3]].
M = [ 8 5 ; 5 3 ] · det(M) = (8×3) − (5×5)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 7], [8, 6]].
M = [ 8 7 ; 8 6 ] · det(M) = (8×6) − (7×8)

12 questions · Seed 51 · 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 = [[3, 9], [1, 12]].
27
det(M) = (3 × 12) − (9 × 1) = 36 − 9 = 27.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [5, 4]].
17
det(M) = (8 × 4) − (3 × 5) = 32 − 15 = 17.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 1], [4, 9]].
104
det(M) = (12 × 9) − (1 × 4) = 108 − 4 = 104.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 2], [4, 4]].
4
det(M) = (3 × 4) − (2 × 4) = 12 − 8 = 4.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [4, 12]].
36
det(M) = (6 × 12) − (9 × 4) = 72 − 36 = 36.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [7, 9]].
-16
det(M) = (6 × 9) − (10 × 7) = 54 − 70 = -16.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 9], [6, 7]].
9
det(M) = (9 × 7) − (9 × 6) = 63 − 54 = 9.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [10, 3]].
-49
det(M) = (7 × 3) − (7 × 10) = 21 − 70 = -49.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 7], [7, 9]].
59
det(M) = (12 × 9) − (7 × 7) = 108 − 49 = 59.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 1], [7, 11]].
125
det(M) = (12 × 11) − (1 × 7) = 132 − 7 = 125.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [5, 3]].
-1
det(M) = (8 × 3) − (5 × 5) = 24 − 25 = -1.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 7], [8, 6]].
-8
det(M) = (8 × 6) − (7 × 8) = 48 − 56 = -8.

12 questions · Seed 51 · Age guidance, not curriculum certification