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

12 questions · Seed 104739 · 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 = [[8, 3], [4, 10]].
68
det(M) = (8 × 10) − (3 × 4) = 80 − 12 = 68.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 7], [10, 6]].
-10
det(M) = (10 × 6) − (7 × 10) = 60 − 70 = -10.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 6], [1, 12]].
114
det(M) = (10 × 12) − (6 × 1) = 120 − 6 = 114.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 9], [8, 9]].
0
det(M) = (8 × 9) − (9 × 8) = 72 − 72 = 0.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 5], [10, 10]].
40
det(M) = (9 × 10) − (5 × 10) = 90 − 50 = 40.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [6, 2]].
-8
det(M) = (11 × 2) − (5 × 6) = 22 − 30 = -8.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 7], [1, 3]].
8
det(M) = (5 × 3) − (7 × 1) = 15 − 7 = 8.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 4], [3, 2]].
8
det(M) = (10 × 2) − (4 × 3) = 20 − 12 = 8.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 3], [6, 6]].
42
det(M) = (10 × 6) − (3 × 6) = 60 − 18 = 42.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 9], [4, 10]].
-16
det(M) = (2 × 10) − (9 × 4) = 20 − 36 = -16.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [7, 12]].
-4
det(M) = (2 × 12) − (4 × 7) = 24 − 28 = -4.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 6], [8, 11]].
73
det(M) = (11 × 11) − (6 × 8) = 121 − 48 = 73.

12 questions · Seed 104739 · 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 = [[8, 3], [4, 10]].
M = [ 8 3 ; 4 10 ] · det(M) = (8×10) − (3×4)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 7], [10, 6]].
M = [ 10 7 ; 10 6 ] · det(M) = (10×6) − (7×10)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 6], [1, 12]].
M = [ 10 6 ; 1 12 ] · det(M) = (10×12) − (6×1)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 9], [8, 9]].
M = [ 8 9 ; 8 9 ] · det(M) = (8×9) − (9×8)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 5], [10, 10]].
M = [ 9 5 ; 10 10 ] · det(M) = (9×10) − (5×10)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [6, 2]].
M = [ 11 5 ; 6 2 ] · det(M) = (11×2) − (5×6)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 7], [1, 3]].
M = [ 5 7 ; 1 3 ] · det(M) = (5×3) − (7×1)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 4], [3, 2]].
M = [ 10 4 ; 3 2 ] · det(M) = (10×2) − (4×3)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 3], [6, 6]].
M = [ 10 3 ; 6 6 ] · det(M) = (10×6) − (3×6)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 9], [4, 10]].
M = [ 2 9 ; 4 10 ] · det(M) = (2×10) − (9×4)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [7, 12]].
M = [ 2 4 ; 7 12 ] · det(M) = (2×12) − (4×7)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 6], [8, 11]].
M = [ 11 6 ; 8 11 ] · det(M) = (11×11) − (6×8)

12 questions · Seed 104739 · 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 = [[8, 3], [4, 10]].
68
det(M) = (8 × 10) − (3 × 4) = 80 − 12 = 68.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 7], [10, 6]].
-10
det(M) = (10 × 6) − (7 × 10) = 60 − 70 = -10.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 6], [1, 12]].
114
det(M) = (10 × 12) − (6 × 1) = 120 − 6 = 114.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 9], [8, 9]].
0
det(M) = (8 × 9) − (9 × 8) = 72 − 72 = 0.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 5], [10, 10]].
40
det(M) = (9 × 10) − (5 × 10) = 90 − 50 = 40.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [6, 2]].
-8
det(M) = (11 × 2) − (5 × 6) = 22 − 30 = -8.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 7], [1, 3]].
8
det(M) = (5 × 3) − (7 × 1) = 15 − 7 = 8.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 4], [3, 2]].
8
det(M) = (10 × 2) − (4 × 3) = 20 − 12 = 8.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 3], [6, 6]].
42
det(M) = (10 × 6) − (3 × 6) = 60 − 18 = 42.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 9], [4, 10]].
-16
det(M) = (2 × 10) − (9 × 4) = 20 − 36 = -16.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [7, 12]].
-4
det(M) = (2 × 12) − (4 × 7) = 24 − 28 = -4.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 6], [8, 11]].
73
det(M) = (11 × 11) − (6 × 8) = 121 − 48 = 73.

12 questions · Seed 104739 · Age guidance, not curriculum certification