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

12 questions · Seed 61 · 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 = [[12, 10], [3, 10]].
90
det(M) = (12 × 10) − (10 × 3) = 120 − 30 = 90.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 5], [2, 10]].
10
det(M) = (2 × 10) − (5 × 2) = 20 − 10 = 10.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [10, 7]].
57
det(M) = (11 × 7) − (2 × 10) = 77 − 20 = 57.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 8], [4, 3]].
-20
det(M) = (4 × 3) − (8 × 4) = 12 − 32 = -20.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 6], [2, 4]].
12
det(M) = (6 × 4) − (6 × 2) = 24 − 12 = 12.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [6, 5]].
-19
det(M) = (7 × 5) − (9 × 6) = 35 − 54 = -19.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 1], [3, 8]].
29
det(M) = (4 × 8) − (1 × 3) = 32 − 3 = 29.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [10, 2]].
-36
det(M) = (2 × 2) − (4 × 10) = 4 − 40 = -36.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 10], [6, 11]].
39
det(M) = (9 × 11) − (10 × 6) = 99 − 60 = 39.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 9], [8, 8]].
-8
det(M) = (8 × 8) − (9 × 8) = 64 − 72 = -8.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 1], [7, 8]].
9
det(M) = (2 × 8) − (1 × 7) = 16 − 7 = 9.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 3], [6, 12]].
18
det(M) = (3 × 12) − (3 × 6) = 36 − 18 = 18.

12 questions · Seed 61 · 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 = [[12, 10], [3, 10]].
M = [ 12 10 ; 3 10 ] · det(M) = (12×10) − (10×3)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 5], [2, 10]].
M = [ 2 5 ; 2 10 ] · det(M) = (2×10) − (5×2)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [10, 7]].
M = [ 11 2 ; 10 7 ] · det(M) = (11×7) − (2×10)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 8], [4, 3]].
M = [ 4 8 ; 4 3 ] · det(M) = (4×3) − (8×4)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 6], [2, 4]].
M = [ 6 6 ; 2 4 ] · det(M) = (6×4) − (6×2)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [6, 5]].
M = [ 7 9 ; 6 5 ] · det(M) = (7×5) − (9×6)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 1], [3, 8]].
M = [ 4 1 ; 3 8 ] · det(M) = (4×8) − (1×3)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [10, 2]].
M = [ 2 4 ; 10 2 ] · det(M) = (2×2) − (4×10)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 10], [6, 11]].
M = [ 9 10 ; 6 11 ] · det(M) = (9×11) − (10×6)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 9], [8, 8]].
M = [ 8 9 ; 8 8 ] · det(M) = (8×8) − (9×8)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 1], [7, 8]].
M = [ 2 1 ; 7 8 ] · det(M) = (2×8) − (1×7)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 3], [6, 12]].
M = [ 3 3 ; 6 12 ] · det(M) = (3×12) − (3×6)

12 questions · Seed 61 · 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 = [[12, 10], [3, 10]].
90
det(M) = (12 × 10) − (10 × 3) = 120 − 30 = 90.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 5], [2, 10]].
10
det(M) = (2 × 10) − (5 × 2) = 20 − 10 = 10.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [10, 7]].
57
det(M) = (11 × 7) − (2 × 10) = 77 − 20 = 57.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 8], [4, 3]].
-20
det(M) = (4 × 3) − (8 × 4) = 12 − 32 = -20.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 6], [2, 4]].
12
det(M) = (6 × 4) − (6 × 2) = 24 − 12 = 12.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [6, 5]].
-19
det(M) = (7 × 5) − (9 × 6) = 35 − 54 = -19.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 1], [3, 8]].
29
det(M) = (4 × 8) − (1 × 3) = 32 − 3 = 29.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [10, 2]].
-36
det(M) = (2 × 2) − (4 × 10) = 4 − 40 = -36.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 10], [6, 11]].
39
det(M) = (9 × 11) − (10 × 6) = 99 − 60 = 39.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 9], [8, 8]].
-8
det(M) = (8 × 8) − (9 × 8) = 64 − 72 = -8.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 1], [7, 8]].
9
det(M) = (2 × 8) − (1 × 7) = 16 − 7 = 9.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 3], [6, 12]].
18
det(M) = (3 × 12) − (3 × 6) = 36 − 18 = 18.

12 questions · Seed 61 · Age guidance, not curriculum certification