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

12 questions · Seed 45 · 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 = [[2, 2], [9, 3]].
-12
det(M) = (2 × 3) − (2 × 9) = 6 − 18 = -12.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [9, 6]].
-54
det(M) = (6 × 6) − (10 × 9) = 36 − 90 = -54.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 9], [9, 7]].
-53
det(M) = (4 × 7) − (9 × 9) = 28 − 81 = -53.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 9], [2, 10]].
32
det(M) = (5 × 10) − (9 × 2) = 50 − 18 = 32.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [1, 5]].
6
det(M) = (2 × 5) − (4 × 1) = 10 − 4 = 6.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [10, 3]].
-25
det(M) = (5 × 3) − (4 × 10) = 15 − 40 = -25.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [3, 12]].
45
det(M) = (6 × 12) − (9 × 3) = 72 − 27 = 45.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [5, 10]].
95
det(M) = (11 × 10) − (3 × 5) = 110 − 15 = 95.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [3, 5]].
10
det(M) = (5 × 5) − (5 × 3) = 25 − 15 = 10.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 3], [9, 2]].
-17
det(M) = (5 × 2) − (3 × 9) = 10 − 27 = -17.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [9, 6]].
21
det(M) = (11 × 6) − (5 × 9) = 66 − 45 = 21.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 4], [10, 2]].
-16
det(M) = (12 × 2) − (4 × 10) = 24 − 40 = -16.

12 questions · Seed 45 · 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 = [[2, 2], [9, 3]].
M = [ 2 2 ; 9 3 ] · det(M) = (2×3) − (2×9)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [9, 6]].
M = [ 6 10 ; 9 6 ] · det(M) = (6×6) − (10×9)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 9], [9, 7]].
M = [ 4 9 ; 9 7 ] · det(M) = (4×7) − (9×9)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 9], [2, 10]].
M = [ 5 9 ; 2 10 ] · det(M) = (5×10) − (9×2)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [1, 5]].
M = [ 2 4 ; 1 5 ] · det(M) = (2×5) − (4×1)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [10, 3]].
M = [ 5 4 ; 10 3 ] · det(M) = (5×3) − (4×10)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [3, 12]].
M = [ 6 9 ; 3 12 ] · det(M) = (6×12) − (9×3)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [5, 10]].
M = [ 11 3 ; 5 10 ] · det(M) = (11×10) − (3×5)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [3, 5]].
M = [ 5 5 ; 3 5 ] · det(M) = (5×5) − (5×3)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 3], [9, 2]].
M = [ 5 3 ; 9 2 ] · det(M) = (5×2) − (3×9)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [9, 6]].
M = [ 11 5 ; 9 6 ] · det(M) = (11×6) − (5×9)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 4], [10, 2]].
M = [ 12 4 ; 10 2 ] · det(M) = (12×2) − (4×10)

12 questions · Seed 45 · 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 = [[2, 2], [9, 3]].
-12
det(M) = (2 × 3) − (2 × 9) = 6 − 18 = -12.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [9, 6]].
-54
det(M) = (6 × 6) − (10 × 9) = 36 − 90 = -54.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 9], [9, 7]].
-53
det(M) = (4 × 7) − (9 × 9) = 28 − 81 = -53.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 9], [2, 10]].
32
det(M) = (5 × 10) − (9 × 2) = 50 − 18 = 32.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 4], [1, 5]].
6
det(M) = (2 × 5) − (4 × 1) = 10 − 4 = 6.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 4], [10, 3]].
-25
det(M) = (5 × 3) − (4 × 10) = 15 − 40 = -25.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 9], [3, 12]].
45
det(M) = (6 × 12) − (9 × 3) = 72 − 27 = 45.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 3], [5, 10]].
95
det(M) = (11 × 10) − (3 × 5) = 110 − 15 = 95.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [3, 5]].
10
det(M) = (5 × 5) − (5 × 3) = 25 − 15 = 10.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 3], [9, 2]].
-17
det(M) = (5 × 2) − (3 × 9) = 10 − 27 = -17.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[11, 5], [9, 6]].
21
det(M) = (11 × 6) − (5 × 9) = 66 − 45 = 21.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 4], [10, 2]].
-16
det(M) = (12 × 2) − (4 × 10) = 24 − 40 = -16.

12 questions · Seed 45 · Age guidance, not curriculum certification