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

12 questions · Seed 104740 · 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 = [[10, 9], [2, 5]].
32
det(M) = (10 × 5) − (9 × 2) = 50 − 18 = 32.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [3, 12]].
45
det(M) = (5 × 12) − (5 × 3) = 60 − 15 = 45.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 2], [2, 4]].
44
det(M) = (12 × 4) − (2 × 2) = 48 − 4 = 44.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 5], [9, 9]].
36
det(M) = (9 × 9) − (5 × 9) = 81 − 45 = 36.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 2], [9, 7]].
45
det(M) = (9 × 7) − (2 × 9) = 63 − 18 = 45.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 1], [8, 10]].
102
det(M) = (11 × 10) − (1 × 8) = 110 − 8 = 102.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [9, 3]].
-57
det(M) = (5 × 3) − (8 × 9) = 15 − 72 = -57.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 4], [8, 2]].
-24
det(M) = (4 × 2) − (4 × 8) = 8 − 32 = -24.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [3, 10]].
64
det(M) = (7 × 10) − (2 × 3) = 70 − 6 = 64.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [6, 11]].
91
det(M) = (11 × 11) − (5 × 6) = 121 − 30 = 91.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 6], [5, 7]].
33
det(M) = (9 × 7) − (6 × 5) = 63 − 30 = 33.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [2, 3]].
0
det(M) = (2 × 3) − (3 × 2) = 6 − 6 = 0.

12 questions · Seed 104740 · 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 = [[10, 9], [2, 5]].
M = [ 10 9 ; 2 5 ] · det(M) = (10×5) − (9×2)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [3, 12]].
M = [ 5 5 ; 3 12 ] · det(M) = (5×12) − (5×3)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 2], [2, 4]].
M = [ 12 2 ; 2 4 ] · det(M) = (12×4) − (2×2)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 5], [9, 9]].
M = [ 9 5 ; 9 9 ] · det(M) = (9×9) − (5×9)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 2], [9, 7]].
M = [ 9 2 ; 9 7 ] · det(M) = (9×7) − (2×9)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 1], [8, 10]].
M = [ 11 1 ; 8 10 ] · det(M) = (11×10) − (1×8)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [9, 3]].
M = [ 5 8 ; 9 3 ] · det(M) = (5×3) − (8×9)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 4], [8, 2]].
M = [ 4 4 ; 8 2 ] · det(M) = (4×2) − (4×8)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [3, 10]].
M = [ 7 2 ; 3 10 ] · det(M) = (7×10) − (2×3)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [6, 11]].
M = [ 11 5 ; 6 11 ] · det(M) = (11×11) − (5×6)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 6], [5, 7]].
M = [ 9 6 ; 5 7 ] · det(M) = (9×7) − (6×5)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [2, 3]].
M = [ 2 3 ; 2 3 ] · det(M) = (2×3) − (3×2)

12 questions · Seed 104740 · 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 = [[10, 9], [2, 5]].
32
det(M) = (10 × 5) − (9 × 2) = 50 − 18 = 32.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [3, 12]].
45
det(M) = (5 × 12) − (5 × 3) = 60 − 15 = 45.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 2], [2, 4]].
44
det(M) = (12 × 4) − (2 × 2) = 48 − 4 = 44.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 5], [9, 9]].
36
det(M) = (9 × 9) − (5 × 9) = 81 − 45 = 36.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 2], [9, 7]].
45
det(M) = (9 × 7) − (2 × 9) = 63 − 18 = 45.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 1], [8, 10]].
102
det(M) = (11 × 10) − (1 × 8) = 110 − 8 = 102.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [9, 3]].
-57
det(M) = (5 × 3) − (8 × 9) = 15 − 72 = -57.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 4], [8, 2]].
-24
det(M) = (4 × 2) − (4 × 8) = 8 − 32 = -24.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 2], [3, 10]].
64
det(M) = (7 × 10) − (2 × 3) = 70 − 6 = 64.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [6, 11]].
91
det(M) = (11 × 11) − (5 × 6) = 121 − 30 = 91.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 6], [5, 7]].
33
det(M) = (9 × 7) − (6 × 5) = 63 − 30 = 33.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [2, 3]].
0
det(M) = (2 × 3) − (3 × 2) = 6 − 6 = 0.

12 questions · Seed 104740 · Age guidance, not curriculum certification