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.

New variation Try interactive challenge Browse templates

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

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

12 questions · Seed 104736 · 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 = [[6, 8], [10, 3]].
-62
det(M) = (6 × 3) − (8 × 10) = 18 − 80 = -62.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [6, 8]].
-44
det(M) = (2 × 8) − (10 × 6) = 16 − 60 = -44.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 3], [9, 9]].
18
det(M) = (5 × 9) − (3 × 9) = 45 − 27 = 18.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 6], [9, 4]].
-42
det(M) = (3 × 4) − (6 × 9) = 12 − 54 = -42.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [7, 4]].
-16
det(M) = (10 × 4) − (8 × 7) = 40 − 56 = -16.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 2], [9, 4]].
22
det(M) = (10 × 4) − (2 × 9) = 40 − 18 = 22.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [5, 12]].
81
det(M) = (8 × 12) − (3 × 5) = 96 − 15 = 81.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 6], [6, 12]].
48
det(M) = (7 × 12) − (6 × 6) = 84 − 36 = 48.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 4], [10, 5]].
5
det(M) = (9 × 5) − (4 × 10) = 45 − 40 = 5.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 9], [6, 7]].
23
det(M) = (11 × 7) − (9 × 6) = 77 − 54 = 23.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 1], [9, 7]].
61
det(M) = (10 × 7) − (1 × 9) = 70 − 9 = 61.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [6, 5]].
-3
det(M) = (9 × 5) − (8 × 6) = 45 − 48 = -3.

12 questions · Seed 104736 · 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 = [[6, 8], [10, 3]].
M = [ 6 8 ; 10 3 ] · det(M) = (6×3) − (8×10)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [6, 8]].
M = [ 2 10 ; 6 8 ] · det(M) = (2×8) − (10×6)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 3], [9, 9]].
M = [ 5 3 ; 9 9 ] · det(M) = (5×9) − (3×9)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 6], [9, 4]].
M = [ 3 6 ; 9 4 ] · det(M) = (3×4) − (6×9)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [7, 4]].
M = [ 10 8 ; 7 4 ] · det(M) = (10×4) − (8×7)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 2], [9, 4]].
M = [ 10 2 ; 9 4 ] · det(M) = (10×4) − (2×9)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [5, 12]].
M = [ 8 3 ; 5 12 ] · det(M) = (8×12) − (3×5)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 6], [6, 12]].
M = [ 7 6 ; 6 12 ] · det(M) = (7×12) − (6×6)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 4], [10, 5]].
M = [ 9 4 ; 10 5 ] · det(M) = (9×5) − (4×10)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 9], [6, 7]].
M = [ 11 9 ; 6 7 ] · det(M) = (11×7) − (9×6)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 1], [9, 7]].
M = [ 10 1 ; 9 7 ] · det(M) = (10×7) − (1×9)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [6, 5]].
M = [ 9 8 ; 6 5 ] · det(M) = (9×5) − (8×6)

12 questions · Seed 104736 · 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 = [[6, 8], [10, 3]].
-62
det(M) = (6 × 3) − (8 × 10) = 18 − 80 = -62.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [6, 8]].
-44
det(M) = (2 × 8) − (10 × 6) = 16 − 60 = -44.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 3], [9, 9]].
18
det(M) = (5 × 9) − (3 × 9) = 45 − 27 = 18.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 6], [9, 4]].
-42
det(M) = (3 × 4) − (6 × 9) = 12 − 54 = -42.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [7, 4]].
-16
det(M) = (10 × 4) − (8 × 7) = 40 − 56 = -16.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 2], [9, 4]].
22
det(M) = (10 × 4) − (2 × 9) = 40 − 18 = 22.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [5, 12]].
81
det(M) = (8 × 12) − (3 × 5) = 96 − 15 = 81.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 6], [6, 12]].
48
det(M) = (7 × 12) − (6 × 6) = 84 − 36 = 48.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 4], [10, 5]].
5
det(M) = (9 × 5) − (4 × 10) = 45 − 40 = 5.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 9], [6, 7]].
23
det(M) = (11 × 7) − (9 × 6) = 77 − 54 = 23.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 1], [9, 7]].
61
det(M) = (10 × 7) − (1 × 9) = 70 − 9 = 61.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [6, 5]].
-3
det(M) = (9 × 5) − (8 × 6) = 45 − 48 = -3.

12 questions · Seed 104736 · Age guidance, not curriculum certification