Last reviewed: 7 November 2026
Updated November 2026. These Grade 9 matrices notes explain what a matrix is, how to state its order, how to name the position of each element, when two matrices can be added or subtracted, and how to do it. A matrix is a rectangular arrangement of numbers in rows and columns. A matrix with 2 rows and 3 columns has order 2 × 3, always written rows first.
The examples and questions are original practice for Kenyan junior school learners, not an official paper. For the other Grade 9 maths topics, see our Grade 9 maths revision guide and the Grade 9 notes hub.
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What the Grade 9 Curriculum Covers
In the Kenya Institute of Curriculum Development’s Grade 9 Mathematics design, Matrices is the first sub-strand under Algebra. It covers the order of a matrix, the position of items, compatibility of matrices, and addition and subtraction, with examples such as football league tables, travel schedules and shopping lists. The design is listed on the KICD Grade Nine curriculum designs page. Matrix multiplication, determinants and inverses are not part of this Grade 9 sub-strand, so they are left out here.
What Is a Matrix?
Any table of numbers arranged in rows and columns can be written as a matrix. Here is a made-up league table for two teams:
| Team | Won | Drawn | Lost |
|---|---|---|---|
| Simba FC | 5 | 2 | 1 |
| Tausi FC | 3 | 4 | 1 |
Removing the labels gives the matrix with first row (5 2 1) and second row (3 4 1). The rows stand for teams and the columns for results. Knowing what the rows and columns represent is just as important as the numbers.
Order of a Matrix
The order is number of rows × number of columns, as defined in OpenStax Precalculus’s section on matrices and matrix operations.
- The league matrix above has 2 rows and 3 columns: order 2 × 3.
- A matrix with one row such as (4 7 9) is a row matrix of order 1 × 3.
- A matrix with one column of three numbers is a column matrix of order 3 × 1.
- A matrix with equal rows and columns, such as 2 × 2, is a square matrix.
A 2 × 3 matrix and a 3 × 2 matrix are different orders. Writing columns first is a common slip.
Position of Elements
Each number in a matrix is an element. Its position is given by its row, then its column. In the league matrix, the element in row 2, column 1 is 3 (Tausi FC’s wins). The element in row 1, column 3 is 1 (Simba FC’s losses). Some books write the element in row i, column j as aij, so a21 = 3.
Compatibility for Addition and Subtraction
Two matrices can be added or subtracted only if they have the same order. A 2 × 3 matrix can be added to another 2 × 3 matrix, but not to a 3 × 2 or 2 × 2 matrix, because some elements would have no partner. The rows and columns must also stand for the same things, or the answer has no meaning.
Adding and Subtracting Matrices
Add or subtract the elements in the same positions. The answer has the same order.
Worked example: two rounds of matches
First round results: Simba (5 2 1), Tausi (3 4 1). Second round: Simba (2 1 0), Tausi (1 1 1). Total:
- Row 1: (5 + 2, 2 + 1, 1 + 0) = (7 3 1)
- Row 2: (3 + 1, 4 + 1, 1 + 1) = (4 5 2)
So after both rounds Simba has won 7, drawn 3 and lost 1.
Worked example: stock in a shop
In this made-up example a duka starts the week with (40 25 60) packets of maize flour, rice and sugar. It sells (28 19 45). Stock left = (40 − 28, 25 − 19, 60 − 45) = (12 6 15). Subtraction of matrices models “opening minus sold” neatly.
Worked example: a 2 × 2 subtraction
A has rows (7 −2) and (0 5). B has rows (3 4) and (−1 6). A − B has rows (7 − 3, −2 − 4) = (4 −6) and (0 − (−1), 5 − 6) = (1 −1). Take care with negative signs: subtracting a negative is adding.
Original Practice Questions With Worked Answers
- State the order of a matrix with 4 rows and 2 columns. 4 × 2.
- In a matrix with rows (6 1 8) and (2 9 4), what is the element in row 2, column 3? 4.
- Can a 2 × 2 matrix be added to a 2 × 1 matrix? No. They have different orders.
- Add (3 −1 4) and (2 5 −6). (5 4 −2).
- A school has (120 95) boys and girls in Grade 8 and (110 102) in Grade 9. Write the total as a row matrix. (230 197).
- Find P − Q if P has rows (9 3) and (4 0), and Q has rows (5 3) and (6 −2). Rows (4 0) and (−2 2).
Cover the answers and attempt each question first. For timed practice, use the Grade 9 revision papers or the Grade 9 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What is the order of a matrix?
The order is the number of rows followed by the number of columns. A matrix with 3 rows and 2 columns has order 3 × 2.
When can two matrices be added?
Only when they have the same order, so that every element has a partner in the same position.
How do you subtract matrices?
Subtract each element of the second matrix from the element in the same position in the first matrix. The answer has the same order.
Is matrix multiplication in Grade 9?
No. The Grade 9 sub-strand covers order, position of elements, compatibility, and addition and subtraction only.