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

12 questions · Seed 44 · 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, 7], [9, 3]].
-42
det(M) = (7 × 3) − (7 × 9) = 21 − 63 = -42.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [8, 9]].
-18
det(M) = (6 × 9) − (9 × 8) = 54 − 72 = -18.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 9], [6, 6]].
12
det(M) = (11 × 6) − (9 × 6) = 66 − 54 = 12.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 5], [7, 12]].
85
det(M) = (10 × 12) − (5 × 7) = 120 − 35 = 85.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [2, 3]].
5
det(M) = (5 × 3) − (5 × 2) = 15 − 10 = 5.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [2, 11]].
53
det(M) = (5 × 11) − (1 × 2) = 55 − 2 = 53.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 8], [5, 7]].
2
det(M) = (6 × 7) − (8 × 5) = 42 − 40 = 2.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [4, 10]].
76
det(M) = (8 × 10) − (1 × 4) = 80 − 4 = 76.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 6], [5, 5]].
25
det(M) = (11 × 5) − (6 × 5) = 55 − 30 = 25.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [10, 6]].
-88
det(M) = (2 × 6) − (10 × 10) = 12 − 100 = -88.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 5], [5, 8]].
7
det(M) = (4 × 8) − (5 × 5) = 32 − 25 = 7.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [8, 9]].
37
det(M) = (5 × 9) − (1 × 8) = 45 − 8 = 37.

12 questions · Seed 44 · 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, 7], [9, 3]].
M = [ 7 7 ; 9 3 ] · det(M) = (7×3) − (7×9)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [8, 9]].
M = [ 6 9 ; 8 9 ] · det(M) = (6×9) − (9×8)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 9], [6, 6]].
M = [ 11 9 ; 6 6 ] · det(M) = (11×6) − (9×6)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 5], [7, 12]].
M = [ 10 5 ; 7 12 ] · det(M) = (10×12) − (5×7)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [2, 3]].
M = [ 5 5 ; 2 3 ] · det(M) = (5×3) − (5×2)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [2, 11]].
M = [ 5 1 ; 2 11 ] · det(M) = (5×11) − (1×2)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 8], [5, 7]].
M = [ 6 8 ; 5 7 ] · det(M) = (6×7) − (8×5)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [4, 10]].
M = [ 8 1 ; 4 10 ] · det(M) = (8×10) − (1×4)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 6], [5, 5]].
M = [ 11 6 ; 5 5 ] · det(M) = (11×5) − (6×5)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [10, 6]].
M = [ 2 10 ; 10 6 ] · det(M) = (2×6) − (10×10)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 5], [5, 8]].
M = [ 4 5 ; 5 8 ] · det(M) = (4×8) − (5×5)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [8, 9]].
M = [ 5 1 ; 8 9 ] · det(M) = (5×9) − (1×8)

12 questions · Seed 44 · 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, 7], [9, 3]].
-42
det(M) = (7 × 3) − (7 × 9) = 21 − 63 = -42.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [8, 9]].
-18
det(M) = (6 × 9) − (9 × 8) = 54 − 72 = -18.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 9], [6, 6]].
12
det(M) = (11 × 6) − (9 × 6) = 66 − 54 = 12.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 5], [7, 12]].
85
det(M) = (10 × 12) − (5 × 7) = 120 − 35 = 85.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [2, 3]].
5
det(M) = (5 × 3) − (5 × 2) = 15 − 10 = 5.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [2, 11]].
53
det(M) = (5 × 11) − (1 × 2) = 55 − 2 = 53.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 8], [5, 7]].
2
det(M) = (6 × 7) − (8 × 5) = 42 − 40 = 2.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 1], [4, 10]].
76
det(M) = (8 × 10) − (1 × 4) = 80 − 4 = 76.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 6], [5, 5]].
25
det(M) = (11 × 5) − (6 × 5) = 55 − 30 = 25.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [10, 6]].
-88
det(M) = (2 × 6) − (10 × 10) = 12 − 100 = -88.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 5], [5, 8]].
7
det(M) = (4 × 8) − (5 × 5) = 32 − 25 = 7.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 1], [8, 9]].
37
det(M) = (5 × 9) − (1 × 8) = 45 − 8 = 37.

12 questions · Seed 44 · Age guidance, not curriculum certification