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

12 questions · Seed 55 · 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 = [[2, 8], [6, 8]].
-32
det(M) = (2 × 8) − (8 × 6) = 16 − 48 = -32.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [3, 8]].
18
det(M) = (6 × 8) − (10 × 3) = 48 − 30 = 18.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 7], [5, 12]].
73
det(M) = (9 × 12) − (7 × 5) = 108 − 35 = 73.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [1, 2]].
2
det(M) = (5 × 2) − (8 × 1) = 10 − 8 = 2.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [1, 4]].
27
det(M) = (8 × 4) − (5 × 1) = 32 − 5 = 27.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 10], [2, 9]].
43
det(M) = (7 × 9) − (10 × 2) = 63 − 20 = 43.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [10, 2]].
-36
det(M) = (2 × 2) − (4 × 10) = 4 − 40 = -36.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [3, 5]].
25
det(M) = (8 × 5) − (5 × 3) = 40 − 15 = 25.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 7], [2, 6]].
52
det(M) = (11 × 6) − (7 × 2) = 66 − 14 = 52.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 6], [10, 11]].
50
det(M) = (10 × 11) − (6 × 10) = 110 − 60 = 50.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [9, 2]].
-4
det(M) = (7 × 2) − (2 × 9) = 14 − 18 = -4.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [5, 10]].
5
det(M) = (2 × 10) − (3 × 5) = 20 − 15 = 5.

12 questions · Seed 55 · 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 = [[2, 8], [6, 8]].
M = [ 2 8 ; 6 8 ] · det(M) = (2×8) − (8×6)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [3, 8]].
M = [ 6 10 ; 3 8 ] · det(M) = (6×8) − (10×3)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 7], [5, 12]].
M = [ 9 7 ; 5 12 ] · det(M) = (9×12) − (7×5)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [1, 2]].
M = [ 5 8 ; 1 2 ] · det(M) = (5×2) − (8×1)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [1, 4]].
M = [ 8 5 ; 1 4 ] · det(M) = (8×4) − (5×1)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 10], [2, 9]].
M = [ 7 10 ; 2 9 ] · det(M) = (7×9) − (10×2)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [10, 2]].
M = [ 2 4 ; 10 2 ] · det(M) = (2×2) − (4×10)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [3, 5]].
M = [ 8 5 ; 3 5 ] · det(M) = (8×5) − (5×3)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 7], [2, 6]].
M = [ 11 7 ; 2 6 ] · det(M) = (11×6) − (7×2)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 6], [10, 11]].
M = [ 10 6 ; 10 11 ] · det(M) = (10×11) − (6×10)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [9, 2]].
M = [ 7 2 ; 9 2 ] · det(M) = (7×2) − (2×9)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [5, 10]].
M = [ 2 3 ; 5 10 ] · det(M) = (2×10) − (3×5)

12 questions · Seed 55 · 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 = [[2, 8], [6, 8]].
-32
det(M) = (2 × 8) − (8 × 6) = 16 − 48 = -32.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [3, 8]].
18
det(M) = (6 × 8) − (10 × 3) = 48 − 30 = 18.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 7], [5, 12]].
73
det(M) = (9 × 12) − (7 × 5) = 108 − 35 = 73.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [1, 2]].
2
det(M) = (5 × 2) − (8 × 1) = 10 − 8 = 2.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [1, 4]].
27
det(M) = (8 × 4) − (5 × 1) = 32 − 5 = 27.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 10], [2, 9]].
43
det(M) = (7 × 9) − (10 × 2) = 63 − 20 = 43.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [10, 2]].
-36
det(M) = (2 × 2) − (4 × 10) = 4 − 40 = -36.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [3, 5]].
25
det(M) = (8 × 5) − (5 × 3) = 40 − 15 = 25.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 7], [2, 6]].
52
det(M) = (11 × 6) − (7 × 2) = 66 − 14 = 52.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 6], [10, 11]].
50
det(M) = (10 × 11) − (6 × 10) = 110 − 60 = 50.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [9, 2]].
-4
det(M) = (7 × 2) − (2 × 9) = 14 − 18 = -4.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [5, 10]].
5
det(M) = (2 × 10) − (3 × 5) = 20 − 15 = 5.

12 questions · Seed 55 · Age guidance, not curriculum certification