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

12 questions · Seed 104733 · 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 = [[9, 7], [2, 3]].
13
det(M) = (9 × 3) − (7 × 2) = 27 − 14 = 13.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [5, 2]].
-14
det(M) = (3 × 2) − (4 × 5) = 6 − 20 = -14.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 7], [4, 5]].
-18
det(M) = (2 × 5) − (7 × 4) = 10 − 28 = -18.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [8, 10]].
72
det(M) = (8 × 10) − (1 × 8) = 80 − 8 = 72.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [5, 5]].
-10
det(M) = (7 × 5) − (9 × 5) = 35 − 45 = -10.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 10], [9, 11]].
-46
det(M) = (4 × 11) − (10 × 9) = 44 − 90 = -46.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 9], [1, 2]].
-1
det(M) = (4 × 2) − (9 × 1) = 8 − 9 = -1.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [3, 12]].
93
det(M) = (8 × 12) − (1 × 3) = 96 − 3 = 93.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [3, 8]].
48
det(M) = (9 × 8) − (8 × 3) = 72 − 24 = 48.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [4, 12]].
120
det(M) = (11 × 12) − (3 × 4) = 132 − 12 = 120.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [10, 5]].
15
det(M) = (7 × 5) − (2 × 10) = 35 − 20 = 15.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 6], [1, 3]].
18
det(M) = (8 × 3) − (6 × 1) = 24 − 6 = 18.

12 questions · Seed 104733 · 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 = [[9, 7], [2, 3]].
M = [ 9 7 ; 2 3 ] · det(M) = (9×3) − (7×2)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [5, 2]].
M = [ 3 4 ; 5 2 ] · det(M) = (3×2) − (4×5)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 7], [4, 5]].
M = [ 2 7 ; 4 5 ] · det(M) = (2×5) − (7×4)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [8, 10]].
M = [ 8 1 ; 8 10 ] · det(M) = (8×10) − (1×8)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [5, 5]].
M = [ 7 9 ; 5 5 ] · det(M) = (7×5) − (9×5)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 10], [9, 11]].
M = [ 4 10 ; 9 11 ] · det(M) = (4×11) − (10×9)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 9], [1, 2]].
M = [ 4 9 ; 1 2 ] · det(M) = (4×2) − (9×1)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [3, 12]].
M = [ 8 1 ; 3 12 ] · det(M) = (8×12) − (1×3)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [3, 8]].
M = [ 9 8 ; 3 8 ] · det(M) = (9×8) − (8×3)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [4, 12]].
M = [ 11 3 ; 4 12 ] · det(M) = (11×12) − (3×4)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [10, 5]].
M = [ 7 2 ; 10 5 ] · det(M) = (7×5) − (2×10)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 6], [1, 3]].
M = [ 8 6 ; 1 3 ] · det(M) = (8×3) − (6×1)

12 questions · Seed 104733 · 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 = [[9, 7], [2, 3]].
13
det(M) = (9 × 3) − (7 × 2) = 27 − 14 = 13.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [5, 2]].
-14
det(M) = (3 × 2) − (4 × 5) = 6 − 20 = -14.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 7], [4, 5]].
-18
det(M) = (2 × 5) − (7 × 4) = 10 − 28 = -18.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [8, 10]].
72
det(M) = (8 × 10) − (1 × 8) = 80 − 8 = 72.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [5, 5]].
-10
det(M) = (7 × 5) − (9 × 5) = 35 − 45 = -10.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 10], [9, 11]].
-46
det(M) = (4 × 11) − (10 × 9) = 44 − 90 = -46.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 9], [1, 2]].
-1
det(M) = (4 × 2) − (9 × 1) = 8 − 9 = -1.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [3, 12]].
93
det(M) = (8 × 12) − (1 × 3) = 96 − 3 = 93.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [3, 8]].
48
det(M) = (9 × 8) − (8 × 3) = 72 − 24 = 48.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [4, 12]].
120
det(M) = (11 × 12) − (3 × 4) = 132 − 12 = 120.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [10, 5]].
15
det(M) = (7 × 5) − (2 × 10) = 35 − 20 = 15.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 6], [1, 3]].
18
det(M) = (8 × 3) − (6 × 1) = 24 − 6 = 18.

12 questions · Seed 104733 · Age guidance, not curriculum certification