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

12 questions · Seed 104744 · 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, 6], [4, 5]].
6
det(M) = (6 × 5) − (6 × 4) = 30 − 24 = 6.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 1], [7, 10]].
83
det(M) = (9 × 10) − (1 × 7) = 90 − 7 = 83.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 7], [10, 8]].
18
det(M) = (11 × 8) − (7 × 10) = 88 − 70 = 18.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 2], [2, 11]].
18
det(M) = (2 × 11) − (2 × 2) = 22 − 4 = 18.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [10, 3]].
-47
det(M) = (11 × 3) − (8 × 10) = 33 − 80 = -47.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [7, 5]].
-10
det(M) = (5 × 5) − (5 × 7) = 25 − 35 = -10.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 10], [5, 3]].
-20
det(M) = (10 × 3) − (10 × 5) = 30 − 50 = -20.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 6], [4, 10]].
96
det(M) = (12 × 10) − (6 × 4) = 120 − 24 = 96.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 7], [2, 10]].
36
det(M) = (5 × 10) − (7 × 2) = 50 − 14 = 36.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 5], [7, 5]].
25
det(M) = (12 × 5) − (5 × 7) = 60 − 35 = 25.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 10], [3, 8]].
34
det(M) = (8 × 8) − (10 × 3) = 64 − 30 = 34.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 8], [4, 7]].
-11
det(M) = (3 × 7) − (8 × 4) = 21 − 32 = -11.

12 questions · Seed 104744 · 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, 6], [4, 5]].
M = [ 6 6 ; 4 5 ] · det(M) = (6×5) − (6×4)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 1], [7, 10]].
M = [ 9 1 ; 7 10 ] · det(M) = (9×10) − (1×7)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 7], [10, 8]].
M = [ 11 7 ; 10 8 ] · det(M) = (11×8) − (7×10)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 2], [2, 11]].
M = [ 2 2 ; 2 11 ] · det(M) = (2×11) − (2×2)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [10, 3]].
M = [ 11 8 ; 10 3 ] · det(M) = (11×3) − (8×10)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [7, 5]].
M = [ 5 5 ; 7 5 ] · det(M) = (5×5) − (5×7)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 10], [5, 3]].
M = [ 10 10 ; 5 3 ] · det(M) = (10×3) − (10×5)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 6], [4, 10]].
M = [ 12 6 ; 4 10 ] · det(M) = (12×10) − (6×4)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 7], [2, 10]].
M = [ 5 7 ; 2 10 ] · det(M) = (5×10) − (7×2)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 5], [7, 5]].
M = [ 12 5 ; 7 5 ] · det(M) = (12×5) − (5×7)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 10], [3, 8]].
M = [ 8 10 ; 3 8 ] · det(M) = (8×8) − (10×3)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 8], [4, 7]].
M = [ 3 8 ; 4 7 ] · det(M) = (3×7) − (8×4)

12 questions · Seed 104744 · 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, 6], [4, 5]].
6
det(M) = (6 × 5) − (6 × 4) = 30 − 24 = 6.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 1], [7, 10]].
83
det(M) = (9 × 10) − (1 × 7) = 90 − 7 = 83.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 7], [10, 8]].
18
det(M) = (11 × 8) − (7 × 10) = 88 − 70 = 18.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 2], [2, 11]].
18
det(M) = (2 × 11) − (2 × 2) = 22 − 4 = 18.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 8], [10, 3]].
-47
det(M) = (11 × 3) − (8 × 10) = 33 − 80 = -47.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [7, 5]].
-10
det(M) = (5 × 5) − (5 × 7) = 25 − 35 = -10.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 10], [5, 3]].
-20
det(M) = (10 × 3) − (10 × 5) = 30 − 50 = -20.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 6], [4, 10]].
96
det(M) = (12 × 10) − (6 × 4) = 120 − 24 = 96.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 7], [2, 10]].
36
det(M) = (5 × 10) − (7 × 2) = 50 − 14 = 36.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 5], [7, 5]].
25
det(M) = (12 × 5) − (5 × 7) = 60 − 35 = 25.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 10], [3, 8]].
34
det(M) = (8 × 8) − (10 × 3) = 64 − 30 = 34.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 8], [4, 7]].
-11
det(M) = (3 × 7) − (8 × 4) = 21 − 32 = -11.

12 questions · Seed 104744 · Age guidance, not curriculum certification