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

12 questions · Seed 104738 · 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, 3], [2, 11]].
27
det(M) = (3 × 11) − (3 × 2) = 33 − 6 = 27.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 9], [8, 9]].
-54
det(M) = (2 × 9) − (9 × 8) = 18 − 72 = -54.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 8], [2, 11]].
72
det(M) = (8 × 11) − (8 × 2) = 88 − 16 = 72.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 8], [5, 2]].
-26
det(M) = (7 × 2) − (8 × 5) = 14 − 40 = -26.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 8], [10, 11]].
-58
det(M) = (2 × 11) − (8 × 10) = 22 − 80 = -58.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 3], [6, 10]].
82
det(M) = (10 × 10) − (3 × 6) = 100 − 18 = 82.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 2], [5, 9]].
8
det(M) = (2 × 9) − (2 × 5) = 18 − 10 = 8.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 7], [8, 5]].
-11
det(M) = (9 × 5) − (7 × 8) = 45 − 56 = -11.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 10], [7, 12]].
-22
det(M) = (4 × 12) − (10 × 7) = 48 − 70 = -22.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 10], [8, 11]].
41
det(M) = (11 × 11) − (10 × 8) = 121 − 80 = 41.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 1], [7, 9]].
11
det(M) = (2 × 9) − (1 × 7) = 18 − 7 = 11.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [5, 3]].
-44
det(M) = (2 × 3) − (10 × 5) = 6 − 50 = -44.

12 questions · Seed 104738 · 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, 3], [2, 11]].
M = [ 3 3 ; 2 11 ] · det(M) = (3×11) − (3×2)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 9], [8, 9]].
M = [ 2 9 ; 8 9 ] · det(M) = (2×9) − (9×8)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 8], [2, 11]].
M = [ 8 8 ; 2 11 ] · det(M) = (8×11) − (8×2)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 8], [5, 2]].
M = [ 7 8 ; 5 2 ] · det(M) = (7×2) − (8×5)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 8], [10, 11]].
M = [ 2 8 ; 10 11 ] · det(M) = (2×11) − (8×10)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 3], [6, 10]].
M = [ 10 3 ; 6 10 ] · det(M) = (10×10) − (3×6)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 2], [5, 9]].
M = [ 2 2 ; 5 9 ] · det(M) = (2×9) − (2×5)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 7], [8, 5]].
M = [ 9 7 ; 8 5 ] · det(M) = (9×5) − (7×8)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 10], [7, 12]].
M = [ 4 10 ; 7 12 ] · det(M) = (4×12) − (10×7)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 10], [8, 11]].
M = [ 11 10 ; 8 11 ] · det(M) = (11×11) − (10×8)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 1], [7, 9]].
M = [ 2 1 ; 7 9 ] · det(M) = (2×9) − (1×7)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [5, 3]].
M = [ 2 10 ; 5 3 ] · det(M) = (2×3) − (10×5)

12 questions · Seed 104738 · 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, 3], [2, 11]].
27
det(M) = (3 × 11) − (3 × 2) = 33 − 6 = 27.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 9], [8, 9]].
-54
det(M) = (2 × 9) − (9 × 8) = 18 − 72 = -54.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 8], [2, 11]].
72
det(M) = (8 × 11) − (8 × 2) = 88 − 16 = 72.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 8], [5, 2]].
-26
det(M) = (7 × 2) − (8 × 5) = 14 − 40 = -26.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 8], [10, 11]].
-58
det(M) = (2 × 11) − (8 × 10) = 22 − 80 = -58.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 3], [6, 10]].
82
det(M) = (10 × 10) − (3 × 6) = 100 − 18 = 82.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 2], [5, 9]].
8
det(M) = (2 × 9) − (2 × 5) = 18 − 10 = 8.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 7], [8, 5]].
-11
det(M) = (9 × 5) − (7 × 8) = 45 − 56 = -11.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 10], [7, 12]].
-22
det(M) = (4 × 12) − (10 × 7) = 48 − 70 = -22.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 10], [8, 11]].
41
det(M) = (11 × 11) − (10 × 8) = 121 − 80 = 41.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 1], [7, 9]].
11
det(M) = (2 × 9) − (1 × 7) = 18 − 7 = 11.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [5, 3]].
-44
det(M) = (2 × 3) − (10 × 5) = 6 − 50 = -44.

12 questions · Seed 104738 · Age guidance, not curriculum certification