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

12 questions · Seed 52 · 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 = [[7, 9], [5, 9]].
18
det(M) = (7 × 9) − (9 × 5) = 63 − 45 = 18.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 2], [3, 11]].
126
det(M) = (12 × 11) − (2 × 3) = 132 − 6 = 126.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 10], [8, 2]].
-60
det(M) = (10 × 2) − (10 × 8) = 20 − 80 = -60.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 7], [4, 8]].
20
det(M) = (6 × 8) − (7 × 4) = 48 − 28 = 20.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 3], [5, 12]].
33
det(M) = (4 × 12) − (3 × 5) = 48 − 15 = 33.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [6, 11]].
9
det(M) = (3 × 11) − (4 × 6) = 33 − 24 = 9.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 4], [10, 10]].
0
det(M) = (4 × 10) − (4 × 10) = 40 − 40 = 0.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 1], [3, 8]].
21
det(M) = (3 × 8) − (1 × 3) = 24 − 3 = 21.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 3], [9, 6]].
-9
det(M) = (3 × 6) − (3 × 9) = 18 − 27 = -9.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 7], [8, 10]].
34
det(M) = (9 × 10) − (7 × 8) = 90 − 56 = 34.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 5], [10, 2]].
-42
det(M) = (4 × 2) − (5 × 10) = 8 − 50 = -42.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 4], [6, 6]].
24
det(M) = (8 × 6) − (4 × 6) = 48 − 24 = 24.

12 questions · Seed 52 · 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 = [[7, 9], [5, 9]].
M = [ 7 9 ; 5 9 ] · det(M) = (7×9) − (9×5)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 2], [3, 11]].
M = [ 12 2 ; 3 11 ] · det(M) = (12×11) − (2×3)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 10], [8, 2]].
M = [ 10 10 ; 8 2 ] · det(M) = (10×2) − (10×8)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 7], [4, 8]].
M = [ 6 7 ; 4 8 ] · det(M) = (6×8) − (7×4)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 3], [5, 12]].
M = [ 4 3 ; 5 12 ] · det(M) = (4×12) − (3×5)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [6, 11]].
M = [ 3 4 ; 6 11 ] · det(M) = (3×11) − (4×6)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 4], [10, 10]].
M = [ 4 4 ; 10 10 ] · det(M) = (4×10) − (4×10)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 1], [3, 8]].
M = [ 3 1 ; 3 8 ] · det(M) = (3×8) − (1×3)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 3], [9, 6]].
M = [ 3 3 ; 9 6 ] · det(M) = (3×6) − (3×9)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 7], [8, 10]].
M = [ 9 7 ; 8 10 ] · det(M) = (9×10) − (7×8)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 5], [10, 2]].
M = [ 4 5 ; 10 2 ] · det(M) = (4×2) − (5×10)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 4], [6, 6]].
M = [ 8 4 ; 6 6 ] · det(M) = (8×6) − (4×6)

12 questions · Seed 52 · 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 = [[7, 9], [5, 9]].
18
det(M) = (7 × 9) − (9 × 5) = 63 − 45 = 18.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 2], [3, 11]].
126
det(M) = (12 × 11) − (2 × 3) = 132 − 6 = 126.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 10], [8, 2]].
-60
det(M) = (10 × 2) − (10 × 8) = 20 − 80 = -60.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 7], [4, 8]].
20
det(M) = (6 × 8) − (7 × 4) = 48 − 28 = 20.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 3], [5, 12]].
33
det(M) = (4 × 12) − (3 × 5) = 48 − 15 = 33.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 4], [6, 11]].
9
det(M) = (3 × 11) − (4 × 6) = 33 − 24 = 9.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 4], [10, 10]].
0
det(M) = (4 × 10) − (4 × 10) = 40 − 40 = 0.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 1], [3, 8]].
21
det(M) = (3 × 8) − (1 × 3) = 24 − 3 = 21.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 3], [9, 6]].
-9
det(M) = (3 × 6) − (3 × 9) = 18 − 27 = -9.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 7], [8, 10]].
34
det(M) = (9 × 10) − (7 × 8) = 90 − 56 = 34.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 5], [10, 2]].
-42
det(M) = (4 × 2) − (5 × 10) = 8 − 50 = -42.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 4], [6, 6]].
24
det(M) = (8 × 6) − (4 × 6) = 48 − 24 = 24.

12 questions · Seed 52 · Age guidance, not curriculum certification