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

12 questions · Seed 42 · 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, 9], [10, 11]].
-24
det(M) = (6 × 11) − (9 × 10) = 66 − 90 = -24.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 7], [9, 5]].
-48
det(M) = (3 × 5) − (7 × 9) = 15 − 63 = -48.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 3], [7, 8]].
3
det(M) = (3 × 8) − (3 × 7) = 24 − 21 = 3.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 6], [6, 2]].
-18
det(M) = (9 × 2) − (6 × 6) = 18 − 36 = -18.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 1], [9, 8]].
79
det(M) = (11 × 8) − (1 × 9) = 88 − 9 = 79.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 1], [1, 4]].
35
det(M) = (9 × 4) − (1 × 1) = 36 − 1 = 35.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [5, 5]].
40
det(M) = (11 × 5) − (3 × 5) = 55 − 15 = 40.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 6], [2, 2]].
-8
det(M) = (2 × 2) − (6 × 2) = 4 − 12 = -8.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 6], [10, 5]].
0
det(M) = (12 × 5) − (6 × 10) = 60 − 60 = 0.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [8, 5]].
16
det(M) = (8 × 5) − (3 × 8) = 40 − 24 = 16.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 2], [1, 11]].
108
det(M) = (10 × 11) − (2 × 1) = 110 − 2 = 108.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [8, 5]].
-7
det(M) = (5 × 5) − (4 × 8) = 25 − 32 = -7.

12 questions · Seed 42 · 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, 9], [10, 11]].
M = [ 6 9 ; 10 11 ] · det(M) = (6×11) − (9×10)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 7], [9, 5]].
M = [ 3 7 ; 9 5 ] · det(M) = (3×5) − (7×9)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 3], [7, 8]].
M = [ 3 3 ; 7 8 ] · det(M) = (3×8) − (3×7)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 6], [6, 2]].
M = [ 9 6 ; 6 2 ] · det(M) = (9×2) − (6×6)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 1], [9, 8]].
M = [ 11 1 ; 9 8 ] · det(M) = (11×8) − (1×9)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 1], [1, 4]].
M = [ 9 1 ; 1 4 ] · det(M) = (9×4) − (1×1)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [5, 5]].
M = [ 11 3 ; 5 5 ] · det(M) = (11×5) − (3×5)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 6], [2, 2]].
M = [ 2 6 ; 2 2 ] · det(M) = (2×2) − (6×2)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 6], [10, 5]].
M = [ 12 6 ; 10 5 ] · det(M) = (12×5) − (6×10)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [8, 5]].
M = [ 8 3 ; 8 5 ] · det(M) = (8×5) − (3×8)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 2], [1, 11]].
M = [ 10 2 ; 1 11 ] · det(M) = (10×11) − (2×1)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [8, 5]].
M = [ 5 4 ; 8 5 ] · det(M) = (5×5) − (4×8)

12 questions · Seed 42 · 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, 9], [10, 11]].
-24
det(M) = (6 × 11) − (9 × 10) = 66 − 90 = -24.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 7], [9, 5]].
-48
det(M) = (3 × 5) − (7 × 9) = 15 − 63 = -48.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 3], [7, 8]].
3
det(M) = (3 × 8) − (3 × 7) = 24 − 21 = 3.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 6], [6, 2]].
-18
det(M) = (9 × 2) − (6 × 6) = 18 − 36 = -18.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 1], [9, 8]].
79
det(M) = (11 × 8) − (1 × 9) = 88 − 9 = 79.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 1], [1, 4]].
35
det(M) = (9 × 4) − (1 × 1) = 36 − 1 = 35.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [5, 5]].
40
det(M) = (11 × 5) − (3 × 5) = 55 − 15 = 40.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 6], [2, 2]].
-8
det(M) = (2 × 2) − (6 × 2) = 4 − 12 = -8.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 6], [10, 5]].
0
det(M) = (12 × 5) − (6 × 10) = 60 − 60 = 0.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 3], [8, 5]].
16
det(M) = (8 × 5) − (3 × 8) = 40 − 24 = 16.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 2], [1, 11]].
108
det(M) = (10 × 11) − (2 × 1) = 110 − 2 = 108.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [8, 5]].
-7
det(M) = (5 × 5) − (4 × 8) = 25 − 32 = -7.

12 questions · Seed 42 · Age guidance, not curriculum certification