CSEC MATHEMATICS · MODULE 2 · LESSON B14

Matrices: Order, Operations and Multiplication

What a matrix is, its order and special types, addition, subtraction, scalar multiplication, multiplying matrices, equal matrices and data matrices.

Intermediate Secondary Level MathematicsM2 5.3M2 5.4M2 5.5≈ 40 min🎮 3 games
Before you start

By the end of this lesson you can…

Step 1 · Watch

Explainer video

5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.

LESSON B14 · EXPLAINER

Matrices: Order, Operations and Multiplication

A spreadsheet is a matrix. Every row of your timetable, every column of prices — matrices organise tables of numbers so you can compute with them all at once.

Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.

Explore in 3D

Matrices

See how a matrix transforms a shape.

Step 2 · Read

Key notes

Copy these into your notebook in your own words — that is how they stick.

Matrix

Rectangular array in rows and columns. Order = rows × columns.

Types

Square, row, column, zero, identity I (1s on the diagonal).

Add / subtract

Same order only; add or subtract corresponding entries.

Scalar multiple

Multiply every entry.

Multiply

Columns of first = rows of second; product order m × p; row × column.

Non-commutative

In general AB ≠ BA; AI = IA = A; (AB)C = A(BC).

Equality

Same order and equal entries → equations for unknowns.

Data matrices

Use matrix multiplication to compute totals such as cost or revenue.

EXAM TIPS & COMMON MISTAKES

  • Check the orders BEFORE multiplying: (2 × 2)(2 × 1) works; (2 × 1)(2 × 2) does not.
  • Never assume AB = BA. If asked, calculate both.
  • Write each multiplication step: 2(1) + 1(−1) — it earns the method mark.
  • Scalar multiplication affects EVERY entry, including zeros that stay zero.
Play & practise

Games

3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Mathematics Arcade.

Step 3 · Practise

Paper 1 practice — multiple choice

8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.

CSEC Paper 01 style · SO 5.3

1. A matrix with 2 rows and 3 columns has order

Answer: A. Order = rows × columns.
CSEC Paper 01 style · SO 5.4

2. If A = 2134 and B = 10−12, then A + B is

Answer: B. Add entries: 2+1,1+03−1,4+2.
CSEC Paper 01 style · SO 5.4

3. If A = 2134 then 3A is

Answer: C. Multiply every entry by 3.
CSEC Paper 01 style · SO 5.4

4. If A = 2134 and B = 10−12, then AB is

Answer: D. (2·1 + 1·(−1), 2·0 + 1·2; 3·1 + 4·(−1), 3·0 + 4·2).
CSEC Paper 01 style · SO 5.3

5. The identity matrix I for 2 × 2 matrices is

Answer: A. Ones on the main diagonal, zeros elsewhere.
CSEC Paper 01 style · SO 5.4

6. Matrix P has order 2 × 1 and matrix Q has order 1 × 2. The order of PQ is

Answer: B. (2 × 1)(1 × 2) → 2 × 2.
CSEC Paper 01 style · SO 5.4

7. Which statement is TRUE for 2 × 2 matrices A and B?

Answer: C. Matrix multiplication is not commutative in general.
CSEC Paper 01 style · SO 5.5

8. x+1,32,y = 5,32,−4. The values of x and y are

Answer: D. x + 1 = 5 → x = 4; y = −4.
Step 4 · Apply

Paper 2 practice — structured questions

Write full answers, then reveal the mark scheme and tick the points you earned (14 marks in total). Show all your working — method marks count. Your answers are saved on this device.

CSEC Paper 02 style · Module 2 (Matrices)

Question 1 [7 marks]

P = 1234 and Q = 0−152.

(a) Calculate P + Q. [1]

MARK SCHEME — (a) (max 1)

(b) Calculate 2P − Q. [2]

MARK SCHEME — (b) (max 2)

(c) Calculate PQ and QP, and state whether PQ = QP. [4]

MARK SCHEME — (c) (max 4)

CSEC Paper 02 style · Module 2 (Data matrices and equality)

Question 2 [7 marks]

A shop sells two items. On Monday it sold 20 of item A and 10 of item B. The unit prices are $5 for A and $8 for B.

(a) Write the sales as a row matrix and the prices as a column matrix. [2]

MARK SCHEME — (a) (max 2)

(b) Multiply the matrices to find the total revenue on Monday. [3]

MARK SCHEME — (b) (max 3)

(c) Given x+2,31,y−1 = 6,31,4, find x and y. [2]

MARK SCHEME — (c) (max 2)

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Sources

Where this topic appears in CSEC papers

Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.