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

12 questions · Seed 50 · 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 = [[7, 5], [7, 5]].
0
det(M) = (7 × 5) − (5 × 7) = 35 − 35 = 0.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 8], [3, 12]].
48
det(M) = (6 × 12) − (8 × 3) = 72 − 24 = 48.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 3], [8, 3]].
-9
det(M) = (5 × 3) − (3 × 8) = 15 − 24 = -9.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 6], [6, 10]].
-6
det(M) = (3 × 10) − (6 × 6) = 30 − 36 = -6.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 3], [5, 7]].
69
det(M) = (12 × 7) − (3 × 5) = 84 − 15 = 69.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 7], [1, 9]].
29
det(M) = (4 × 9) − (7 × 1) = 36 − 7 = 29.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 10], [2, 6]].
46
det(M) = (11 × 6) − (10 × 2) = 66 − 20 = 46.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 9], [9, 12]].
27
det(M) = (9 × 12) − (9 × 9) = 108 − 81 = 27.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [1, 9]].
98
det(M) = (12 × 9) − (10 × 1) = 108 − 10 = 98.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 1], [3, 6]].
21
det(M) = (4 × 6) − (1 × 3) = 24 − 3 = 21.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [4, 3]].
-7
det(M) = (3 × 3) − (4 × 4) = 9 − 16 = -7.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [1, 4]].
19
det(M) = (5 × 4) − (1 × 1) = 20 − 1 = 19.

12 questions · Seed 50 · 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 = [[7, 5], [7, 5]].
M = [ 7 5 ; 7 5 ] · det(M) = (7×5) − (5×7)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 8], [3, 12]].
M = [ 6 8 ; 3 12 ] · det(M) = (6×12) − (8×3)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 3], [8, 3]].
M = [ 5 3 ; 8 3 ] · det(M) = (5×3) − (3×8)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 6], [6, 10]].
M = [ 3 6 ; 6 10 ] · det(M) = (3×10) − (6×6)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 3], [5, 7]].
M = [ 12 3 ; 5 7 ] · det(M) = (12×7) − (3×5)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 7], [1, 9]].
M = [ 4 7 ; 1 9 ] · det(M) = (4×9) − (7×1)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 10], [2, 6]].
M = [ 11 10 ; 2 6 ] · det(M) = (11×6) − (10×2)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 9], [9, 12]].
M = [ 9 9 ; 9 12 ] · det(M) = (9×12) − (9×9)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [1, 9]].
M = [ 12 10 ; 1 9 ] · det(M) = (12×9) − (10×1)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 1], [3, 6]].
M = [ 4 1 ; 3 6 ] · det(M) = (4×6) − (1×3)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [4, 3]].
M = [ 3 4 ; 4 3 ] · det(M) = (3×3) − (4×4)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [1, 4]].
M = [ 5 1 ; 1 4 ] · det(M) = (5×4) − (1×1)

12 questions · Seed 50 · 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 = [[7, 5], [7, 5]].
0
det(M) = (7 × 5) − (5 × 7) = 35 − 35 = 0.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 8], [3, 12]].
48
det(M) = (6 × 12) − (8 × 3) = 72 − 24 = 48.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 3], [8, 3]].
-9
det(M) = (5 × 3) − (3 × 8) = 15 − 24 = -9.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 6], [6, 10]].
-6
det(M) = (3 × 10) − (6 × 6) = 30 − 36 = -6.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 3], [5, 7]].
69
det(M) = (12 × 7) − (3 × 5) = 84 − 15 = 69.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 7], [1, 9]].
29
det(M) = (4 × 9) − (7 × 1) = 36 − 7 = 29.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 10], [2, 6]].
46
det(M) = (11 × 6) − (10 × 2) = 66 − 20 = 46.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 9], [9, 12]].
27
det(M) = (9 × 12) − (9 × 9) = 108 − 81 = 27.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [1, 9]].
98
det(M) = (12 × 9) − (10 × 1) = 108 − 10 = 98.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 1], [3, 6]].
21
det(M) = (4 × 6) − (1 × 3) = 24 − 3 = 21.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [4, 3]].
-7
det(M) = (3 × 3) − (4 × 4) = 9 − 16 = -7.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [1, 4]].
19
det(M) = (5 × 4) − (1 × 1) = 20 − 1 = 19.

12 questions · Seed 50 · Age guidance, not curriculum certification