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

12 questions · Seed 46 · 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 = [[8, 9], [9, 5]].
-41
det(M) = (8 × 5) − (9 × 9) = 40 − 81 = -41.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 5], [7, 7]].
28
det(M) = (9 × 7) − (5 × 7) = 63 − 35 = 28.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 2], [3, 8]].
18
det(M) = (3 × 8) − (2 × 3) = 24 − 6 = 18.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [7, 12]].
3
det(M) = (2 × 12) − (3 × 7) = 24 − 21 = 3.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [2, 2]].
0
det(M) = (5 × 2) − (5 × 2) = 10 − 10 = 0.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 10], [4, 11]].
70
det(M) = (10 × 11) − (10 × 4) = 110 − 40 = 70.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 10], [10, 9]].
-1
det(M) = (11 × 9) − (10 × 10) = 99 − 100 = -1.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [5, 12]].
49
det(M) = (7 × 12) − (7 × 5) = 84 − 35 = 49.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [4, 8]].
0
det(M) = (2 × 8) − (4 × 4) = 16 − 16 = 0.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [8, 11]].
15
det(M) = (5 × 11) − (5 × 8) = 55 − 40 = 15.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [5, 8]].
78
det(M) = (11 × 8) − (2 × 5) = 88 − 10 = 78.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [4, 11]].
68
det(M) = (8 × 11) − (5 × 4) = 88 − 20 = 68.

12 questions · Seed 46 · 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 = [[8, 9], [9, 5]].
M = [ 8 9 ; 9 5 ] · det(M) = (8×5) − (9×9)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 5], [7, 7]].
M = [ 9 5 ; 7 7 ] · det(M) = (9×7) − (5×7)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 2], [3, 8]].
M = [ 3 2 ; 3 8 ] · det(M) = (3×8) − (2×3)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [7, 12]].
M = [ 2 3 ; 7 12 ] · det(M) = (2×12) − (3×7)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [2, 2]].
M = [ 5 5 ; 2 2 ] · det(M) = (5×2) − (5×2)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 10], [4, 11]].
M = [ 10 10 ; 4 11 ] · det(M) = (10×11) − (10×4)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 10], [10, 9]].
M = [ 11 10 ; 10 9 ] · det(M) = (11×9) − (10×10)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [5, 12]].
M = [ 7 7 ; 5 12 ] · det(M) = (7×12) − (7×5)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [4, 8]].
M = [ 2 4 ; 4 8 ] · det(M) = (2×8) − (4×4)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [8, 11]].
M = [ 5 5 ; 8 11 ] · det(M) = (5×11) − (5×8)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [5, 8]].
M = [ 11 2 ; 5 8 ] · det(M) = (11×8) − (2×5)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [4, 11]].
M = [ 8 5 ; 4 11 ] · det(M) = (8×11) − (5×4)

12 questions · Seed 46 · 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 = [[8, 9], [9, 5]].
-41
det(M) = (8 × 5) − (9 × 9) = 40 − 81 = -41.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 5], [7, 7]].
28
det(M) = (9 × 7) − (5 × 7) = 63 − 35 = 28.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 2], [3, 8]].
18
det(M) = (3 × 8) − (2 × 3) = 24 − 6 = 18.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [7, 12]].
3
det(M) = (2 × 12) − (3 × 7) = 24 − 21 = 3.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [2, 2]].
0
det(M) = (5 × 2) − (5 × 2) = 10 − 10 = 0.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 10], [4, 11]].
70
det(M) = (10 × 11) − (10 × 4) = 110 − 40 = 70.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 10], [10, 9]].
-1
det(M) = (11 × 9) − (10 × 10) = 99 − 100 = -1.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [5, 12]].
49
det(M) = (7 × 12) − (7 × 5) = 84 − 35 = 49.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [4, 8]].
0
det(M) = (2 × 8) − (4 × 4) = 16 − 16 = 0.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [8, 11]].
15
det(M) = (5 × 11) − (5 × 8) = 55 − 40 = 15.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 2], [5, 8]].
78
det(M) = (11 × 8) − (2 × 5) = 88 − 10 = 78.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 5], [4, 11]].
68
det(M) = (8 × 11) − (5 × 4) = 88 − 20 = 68.

12 questions · Seed 46 · Age guidance, not curriculum certification