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

12 questions · Seed 54 · 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, 7], [6, 2]].
-36
det(M) = (3 × 2) − (7 × 6) = 6 − 42 = -36.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [8, 11]].
57
det(M) = (11 × 11) − (8 × 8) = 121 − 64 = 57.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 8], [8, 12]].
80
det(M) = (12 × 12) − (8 × 8) = 144 − 64 = 80.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 4], [2, 7]].
62
det(M) = (10 × 7) − (4 × 2) = 70 − 8 = 62.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [2, 11]].
48
det(M) = (6 × 11) − (9 × 2) = 66 − 18 = 48.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [4, 5]].
27
det(M) = (7 × 5) − (2 × 4) = 35 − 8 = 27.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 4], [8, 4]].
8
det(M) = (10 × 4) − (4 × 8) = 40 − 32 = 8.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [2, 9]].
89
det(M) = (11 × 9) − (5 × 2) = 99 − 10 = 89.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 7], [7, 3]].
-25
det(M) = (8 × 3) − (7 × 7) = 24 − 49 = -25.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [10, 2]].
-76
det(M) = (7 × 2) − (9 × 10) = 14 − 90 = -76.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 5], [9, 12]].
-21
det(M) = (2 × 12) − (5 × 9) = 24 − 45 = -21.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 8], [3, 7]].
25
det(M) = (7 × 7) − (8 × 3) = 49 − 24 = 25.

12 questions · Seed 54 · 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, 7], [6, 2]].
M = [ 3 7 ; 6 2 ] · det(M) = (3×2) − (7×6)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [8, 11]].
M = [ 11 8 ; 8 11 ] · det(M) = (11×11) − (8×8)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 8], [8, 12]].
M = [ 12 8 ; 8 12 ] · det(M) = (12×12) − (8×8)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 4], [2, 7]].
M = [ 10 4 ; 2 7 ] · det(M) = (10×7) − (4×2)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [2, 11]].
M = [ 6 9 ; 2 11 ] · det(M) = (6×11) − (9×2)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [4, 5]].
M = [ 7 2 ; 4 5 ] · det(M) = (7×5) − (2×4)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 4], [8, 4]].
M = [ 10 4 ; 8 4 ] · det(M) = (10×4) − (4×8)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [2, 9]].
M = [ 11 5 ; 2 9 ] · det(M) = (11×9) − (5×2)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 7], [7, 3]].
M = [ 8 7 ; 7 3 ] · det(M) = (8×3) − (7×7)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [10, 2]].
M = [ 7 9 ; 10 2 ] · det(M) = (7×2) − (9×10)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 5], [9, 12]].
M = [ 2 5 ; 9 12 ] · det(M) = (2×12) − (5×9)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 8], [3, 7]].
M = [ 7 8 ; 3 7 ] · det(M) = (7×7) − (8×3)

12 questions · Seed 54 · 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, 7], [6, 2]].
-36
det(M) = (3 × 2) − (7 × 6) = 6 − 42 = -36.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [8, 11]].
57
det(M) = (11 × 11) − (8 × 8) = 121 − 64 = 57.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 8], [8, 12]].
80
det(M) = (12 × 12) − (8 × 8) = 144 − 64 = 80.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 4], [2, 7]].
62
det(M) = (10 × 7) − (4 × 2) = 70 − 8 = 62.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [2, 11]].
48
det(M) = (6 × 11) − (9 × 2) = 66 − 18 = 48.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [4, 5]].
27
det(M) = (7 × 5) − (2 × 4) = 35 − 8 = 27.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 4], [8, 4]].
8
det(M) = (10 × 4) − (4 × 8) = 40 − 32 = 8.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [2, 9]].
89
det(M) = (11 × 9) − (5 × 2) = 99 − 10 = 89.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 7], [7, 3]].
-25
det(M) = (8 × 3) − (7 × 7) = 24 − 49 = -25.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [10, 2]].
-76
det(M) = (7 × 2) − (9 × 10) = 14 − 90 = -76.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 5], [9, 12]].
-21
det(M) = (2 × 12) − (5 × 9) = 24 − 45 = -21.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 8], [3, 7]].
25
det(M) = (7 × 7) − (8 × 3) = 49 − 24 = 25.

12 questions · Seed 54 · Age guidance, not curriculum certification