Topic guide · SS 3
Matrices
Introduction to matrices for SS 3: matrix notation, the determinant of a 2 × 2 matrix and common mistakes, with worked examples and practice.
Start the Matrix Operations lesson →Matrices explained
A matrix is a rectangular grid of numbers arranged in rows and columns. Matrices are used to solve systems of equations, transform shapes and power computer graphics.
For a 2 × 2 matrix, the determinant is a single number that tells you, among other things, whether the matrix has an inverse.
Key ideas to remember
- A matrix with m rows and n columns has order m × n.
- Determinant of abcd = ad − bc: leading diagonal product minus the other diagonal product.
- A matrix with determinant 0 has no inverse.
- Matrices of the same order are added by adding matching entries.
Worked example
Find the determinant of the matrix 365−1.
Step 1: Use ad − bc
(3)(−1) − (6)(5)
Step 2: Work it out
= −3 − 30 = −33
Final answer: −33
Practice questions
Have a go, then open the answer to check your working. Every answer was checked by the MathPlug maths engine.
Question 1
Find the determinant of the matrix −5−13−4.
- A17
- B23
- C24
- D−23
Show answer and working
Step 1: Use ad − bc
(−5)(−4) − (−1)(3)
Step 2: Work it out
= 20 − (−3) = 23
Final answer: 23
Question 2
Find the determinant of the matrix −3527.
- A−11
- B−31
- C31
- D−29
Show answer and working
Step 1: Use ad − bc
(−3)(7) − (5)(2)
Step 2: Work it out
= −21 − 10 = −31
Final answer: −31
Question 3
Find the determinant of the matrix 6−33−5.
- A−39
- B21
- C−21
- D−3
Show answer and working
Step 1: Use ad − bc
(6)(−5) − (−3)(3)
Step 2: Work it out
= −30 − (−9) = −21
Final answer: −21
Frequently asked questions
- Is it ad − bc or bc − ad?
- ad − bc: multiply the leading diagonal (top-left to bottom-right) first, then subtract the other diagonal.
- Can any two matrices be multiplied?
- Only when the number of columns in the first equals the number of rows in the second.