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

12 questions · Seed 104729 · 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 = [[8, 7], [6, 5]].
-2
det(M) = (8 × 5) − (7 × 6) = 40 − 42 = -2.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 6], [6, 4]].
4
det(M) = (10 × 4) − (6 × 6) = 40 − 36 = 4.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [5, 8]].
0
det(M) = (5 × 8) − (8 × 5) = 40 − 40 = 0.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 10], [8, 7]].
-24
det(M) = (8 × 7) − (10 × 8) = 56 − 80 = -24.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [1, 11]].
28
det(M) = (3 × 11) − (5 × 1) = 33 − 5 = 28.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 9], [4, 8]].
36
det(M) = (9 × 8) − (9 × 4) = 72 − 36 = 36.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 2], [5, 3]].
20
det(M) = (10 × 3) − (2 × 5) = 30 − 10 = 20.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [6, 6]].
-6
det(M) = (2 × 6) − (3 × 6) = 12 − 18 = -6.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 1], [6, 5]].
14
det(M) = (4 × 5) − (1 × 6) = 20 − 6 = 14.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 6], [3, 12]].
66
det(M) = (7 × 12) − (6 × 3) = 84 − 18 = 66.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [7, 5]].
-14
det(M) = (7 × 5) − (7 × 7) = 35 − 49 = -14.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [3, 2]].
-4
det(M) = (10 × 2) − (8 × 3) = 20 − 24 = -4.

12 questions · Seed 104729 · 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 = [[8, 7], [6, 5]].
M = [ 8 7 ; 6 5 ] · det(M) = (8×5) − (7×6)
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 6], [6, 4]].
M = [ 10 6 ; 6 4 ] · det(M) = (10×4) − (6×6)
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [5, 8]].
M = [ 5 8 ; 5 8 ] · det(M) = (5×8) − (8×5)
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 10], [8, 7]].
M = [ 8 10 ; 8 7 ] · det(M) = (8×7) − (10×8)
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [1, 11]].
M = [ 3 5 ; 1 11 ] · det(M) = (3×11) − (5×1)
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 9], [4, 8]].
M = [ 9 9 ; 4 8 ] · det(M) = (9×8) − (9×4)
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 2], [5, 3]].
M = [ 10 2 ; 5 3 ] · det(M) = (10×3) − (2×5)
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [6, 6]].
M = [ 2 3 ; 6 6 ] · det(M) = (2×6) − (3×6)
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 1], [6, 5]].
M = [ 4 1 ; 6 5 ] · det(M) = (4×5) − (1×6)
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 6], [3, 12]].
M = [ 7 6 ; 3 12 ] · det(M) = (7×12) − (6×3)
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [7, 5]].
M = [ 7 7 ; 7 5 ] · det(M) = (7×5) − (7×7)
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [3, 2]].
M = [ 10 8 ; 3 2 ] · det(M) = (10×2) − (8×3)

12 questions · Seed 104729 · 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 = [[8, 7], [6, 5]].
-2
det(M) = (8 × 5) − (7 × 6) = 40 − 42 = -2.
2. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 6], [6, 4]].
4
det(M) = (10 × 4) − (6 × 6) = 40 − 36 = 4.
3. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[5, 8], [5, 8]].
0
det(M) = (5 × 8) − (8 × 5) = 40 − 40 = 0.
4. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[8, 10], [8, 7]].
-24
det(M) = (8 × 7) − (10 × 8) = 56 − 80 = -24.
5. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[3, 5], [1, 11]].
28
det(M) = (3 × 11) − (5 × 1) = 33 − 5 = 28.
6. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[9, 9], [4, 8]].
36
det(M) = (9 × 8) − (9 × 4) = 72 − 36 = 36.
7. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 2], [5, 3]].
20
det(M) = (10 × 3) − (2 × 5) = 30 − 10 = 20.
8. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[2, 3], [6, 6]].
-6
det(M) = (2 × 6) − (3 × 6) = 12 − 18 = -6.
9. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[4, 1], [6, 5]].
14
det(M) = (4 × 5) − (1 × 6) = 20 − 6 = 14.
10. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 6], [3, 12]].
66
det(M) = (7 × 12) − (6 × 3) = 84 − 18 = 66.
11. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[7, 7], [7, 5]].
-14
det(M) = (7 × 5) − (7 × 7) = 35 − 49 = -14.
12. Calculate the determinant det(M) = ad − bc of the 2×2 matrix M = [[10, 8], [3, 2]].
-4
det(M) = (10 × 2) − (8 × 3) = 20 − 24 = -4.

12 questions · Seed 104729 · Age guidance, not curriculum certification