Back to Further MathematicsPractice this
Paper 1
Matrices & Transformations
Both
Matrix multiplication order matters: AB ≠ BA.
Key Facts
- Determinant = ad - bc for [[a,b],[c,d]]
- Matrix multiplication is not commutative.
- Identity matrix I = [[1,0],[0,1]]
- AA^-1 = A^-1A = I
- det(AB) = det(A) × det(B)
Key Equations
det(A) = ad - bc
A^-1 = (1/det(A)) × [[d, -b],[-c, a]]
Topics Covered
Matrix Operations
What you need to know
- •Add and subtract matrices component-wise.
- •Multiply 2x2 matrices using row × column rule.
- •Find determinant using ad - bc for matrix [[a,b],[c,d]].
- •Matrix multiplication is not commutative: AB ≠ BA.
Exam Tips
- Show working for inverse matrices to collect method marks.
- Check det ≠ 0 before finding inverse.
Inverse Matrices
What you need to know
- •Only matrices with non-zero determinant have inverses.
- •Use formula: A^-1 = (1/det(A)) × [[d,-b],[-c,a]].
- •Check: AA^-1 = I (identity matrix).
Exam Tips
- Swap a and d, negate b and c, then multiply by 1/det.
Matrices as Transformations
What you need to know
- •Matrices represent geometric transformations.
- •Determinant gives the area scale factor.
- •Negative determinant means reflection involved.
Exam Tips
- Link matrix to rotation, reflection, or enlargement.
Key Terms
Determinant
Single value describing scale factor of transformation.
Identity matrix
Matrix that leaves others unchanged when multiplied: [[1,0],[0,1]].
Inverse matrix
Matrix A^-1 that satisfies AA^-1 = I.
Singular matrix
Matrix with determinant 0, so no inverse exists.
Loading practice drills...
Common Exam Questions
Find the determinant of [[3,4],[2,1]].
2 markseasyPaper 1
Model Answer
det = 3×1 - 4×2 = 3 - 8 = -5
What examiners want to see
- ✓Compute ad - bc correctly.
- ✓Show working.
Given A = [[2,3],[1,2]], find A^-1.
3 marksmediumPaper 1
Model Answer
det(A) = 4-3 = 1. A^-1 = [[2,-3],[-1,2]]
What examiners want to see
- ✓Find determinant first.
- ✓Use inverse formula.
Matrix M represents a transformation with det(M) = -4. What does this tell you?
2 marksmediumPaper 1
Model Answer
Area scale factor is 4, and there is a reflection.
What examiners want to see
- ✓Negative means reflection.
- ✓Magnitude is scale factor.
Related Topics
Other topics you might find useful