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

12 questions · Seed 104737 · 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 = [[5, 10], [4, 5]].
-15
det(M) = (5 × 5) − (10 × 4) = 25 − 40 = -15.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 6], [9, 3]].
-45
det(M) = (3 × 3) − (6 × 9) = 9 − 54 = -45.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [1, 9]].
44
det(M) = (6 × 9) − (10 × 1) = 54 − 10 = 44.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 1], [2, 6]].
10
det(M) = (2 × 6) − (1 × 2) = 12 − 2 = 10.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 8], [4, 12]].
-8
det(M) = (2 × 12) − (8 × 4) = 24 − 32 = -8.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [7, 6]].
-5
det(M) = (5 × 6) − (5 × 7) = 30 − 35 = -5.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 2], [7, 9]].
40
det(M) = (6 × 9) − (2 × 7) = 54 − 14 = 40.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 3], [4, 3]].
9
det(M) = (7 × 3) − (3 × 4) = 21 − 12 = 9.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [7, 9]].
-52
det(M) = (2 × 9) − (10 × 7) = 18 − 70 = -52.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 1], [9, 3]].
3
det(M) = (4 × 3) − (1 × 9) = 12 − 9 = 3.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [6, 5]].
-3
det(M) = (9 × 5) − (8 × 6) = 45 − 48 = -3.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [7, 4]].
-62
det(M) = (2 × 4) − (10 × 7) = 8 − 70 = -62.

12 questions · Seed 104737 · 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 = [[5, 10], [4, 5]].
M = [ 5 10 ; 4 5 ] · det(M) = (5×5) − (10×4)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 6], [9, 3]].
M = [ 3 6 ; 9 3 ] · det(M) = (3×3) − (6×9)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [1, 9]].
M = [ 6 10 ; 1 9 ] · det(M) = (6×9) − (10×1)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 1], [2, 6]].
M = [ 2 1 ; 2 6 ] · det(M) = (2×6) − (1×2)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 8], [4, 12]].
M = [ 2 8 ; 4 12 ] · det(M) = (2×12) − (8×4)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [7, 6]].
M = [ 5 5 ; 7 6 ] · det(M) = (5×6) − (5×7)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 2], [7, 9]].
M = [ 6 2 ; 7 9 ] · det(M) = (6×9) − (2×7)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 3], [4, 3]].
M = [ 7 3 ; 4 3 ] · det(M) = (7×3) − (3×4)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [7, 9]].
M = [ 2 10 ; 7 9 ] · det(M) = (2×9) − (10×7)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 1], [9, 3]].
M = [ 4 1 ; 9 3 ] · det(M) = (4×3) − (1×9)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [6, 5]].
M = [ 9 8 ; 6 5 ] · det(M) = (9×5) − (8×6)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [7, 4]].
M = [ 2 10 ; 7 4 ] · det(M) = (2×4) − (10×7)

12 questions · Seed 104737 · 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 = [[5, 10], [4, 5]].
-15
det(M) = (5 × 5) − (10 × 4) = 25 − 40 = -15.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 6], [9, 3]].
-45
det(M) = (3 × 3) − (6 × 9) = 9 − 54 = -45.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [1, 9]].
44
det(M) = (6 × 9) − (10 × 1) = 54 − 10 = 44.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 1], [2, 6]].
10
det(M) = (2 × 6) − (1 × 2) = 12 − 2 = 10.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 8], [4, 12]].
-8
det(M) = (2 × 12) − (8 × 4) = 24 − 32 = -8.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 5], [7, 6]].
-5
det(M) = (5 × 6) − (5 × 7) = 30 − 35 = -5.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 2], [7, 9]].
40
det(M) = (6 × 9) − (2 × 7) = 54 − 14 = 40.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 3], [4, 3]].
9
det(M) = (7 × 3) − (3 × 4) = 21 − 12 = 9.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [7, 9]].
-52
det(M) = (2 × 9) − (10 × 7) = 18 − 70 = -52.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 1], [9, 3]].
3
det(M) = (4 × 3) − (1 × 9) = 12 − 9 = 3.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 8], [6, 5]].
-3
det(M) = (9 × 5) − (8 × 6) = 45 − 48 = -3.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 10], [7, 4]].
-62
det(M) = (2 × 4) − (10 × 7) = 8 − 70 = -62.

12 questions · Seed 104737 · Age guidance, not curriculum certification