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

12 questions · Seed 53 · 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 = [[9, 1], [1, 12]].
107
det(M) = (9 × 12) − (1 × 1) = 108 − 1 = 107.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [7, 10]].
-5
det(M) = (3 × 10) − (5 × 7) = 30 − 35 = -5.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 6], [1, 7]].
64
det(M) = (10 × 7) − (6 × 1) = 70 − 6 = 64.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 9], [6, 5]].
-14
det(M) = (8 × 5) − (9 × 6) = 40 − 54 = -14.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [9, 2]].
-66
det(M) = (12 × 2) − (10 × 9) = 24 − 90 = -66.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [8, 7]].
-38
det(M) = (6 × 7) − (10 × 8) = 42 − 80 = -38.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 4], [8, 8]].
40
det(M) = (9 × 8) − (4 × 8) = 72 − 32 = 40.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 7], [7, 2]].
-25
det(M) = (12 × 2) − (7 × 7) = 24 − 49 = -25.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 9], [7, 9]].
45
det(M) = (12 × 9) − (9 × 7) = 108 − 63 = 45.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [1, 10]].
59
det(M) = (6 × 10) − (1 × 1) = 60 − 1 = 59.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [1, 8]].
49
det(M) = (7 × 8) − (7 × 1) = 56 − 7 = 49.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [2, 10]].
52
det(M) = (7 × 10) − (9 × 2) = 70 − 18 = 52.

12 questions · Seed 53 · 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 = [[9, 1], [1, 12]].
M = [ 9 1 ; 1 12 ] · det(M) = (9×12) − (1×1)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [7, 10]].
M = [ 3 5 ; 7 10 ] · det(M) = (3×10) − (5×7)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 6], [1, 7]].
M = [ 10 6 ; 1 7 ] · det(M) = (10×7) − (6×1)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 9], [6, 5]].
M = [ 8 9 ; 6 5 ] · det(M) = (8×5) − (9×6)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [9, 2]].
M = [ 12 10 ; 9 2 ] · det(M) = (12×2) − (10×9)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [8, 7]].
M = [ 6 10 ; 8 7 ] · det(M) = (6×7) − (10×8)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 4], [8, 8]].
M = [ 9 4 ; 8 8 ] · det(M) = (9×8) − (4×8)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 7], [7, 2]].
M = [ 12 7 ; 7 2 ] · det(M) = (12×2) − (7×7)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 9], [7, 9]].
M = [ 12 9 ; 7 9 ] · det(M) = (12×9) − (9×7)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [1, 10]].
M = [ 6 1 ; 1 10 ] · det(M) = (6×10) − (1×1)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [1, 8]].
M = [ 7 7 ; 1 8 ] · det(M) = (7×8) − (7×1)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [2, 10]].
M = [ 7 9 ; 2 10 ] · det(M) = (7×10) − (9×2)

12 questions · Seed 53 · 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 = [[9, 1], [1, 12]].
107
det(M) = (9 × 12) − (1 × 1) = 108 − 1 = 107.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [7, 10]].
-5
det(M) = (3 × 10) − (5 × 7) = 30 − 35 = -5.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 6], [1, 7]].
64
det(M) = (10 × 7) − (6 × 1) = 70 − 6 = 64.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 9], [6, 5]].
-14
det(M) = (8 × 5) − (9 × 6) = 40 − 54 = -14.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 10], [9, 2]].
-66
det(M) = (12 × 2) − (10 × 9) = 24 − 90 = -66.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 10], [8, 7]].
-38
det(M) = (6 × 7) − (10 × 8) = 42 − 80 = -38.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 4], [8, 8]].
40
det(M) = (9 × 8) − (4 × 8) = 72 − 32 = 40.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 7], [7, 2]].
-25
det(M) = (12 × 2) − (7 × 7) = 24 − 49 = -25.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[12, 9], [7, 9]].
45
det(M) = (12 × 9) − (9 × 7) = 108 − 63 = 45.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[6, 1], [1, 10]].
59
det(M) = (6 × 10) − (1 × 1) = 60 − 1 = 59.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [1, 8]].
49
det(M) = (7 × 8) − (7 × 1) = 56 − 7 = 49.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 9], [2, 10]].
52
det(M) = (7 × 10) − (9 × 2) = 70 − 18 = 52.

12 questions · Seed 53 · Age guidance, not curriculum certification