Free Grade 3 Working with Matrix Multiplication Techniques Worksheets
Free Grade 3 worksheets for Working with Matrix Multiplication Techniques: 12 real questions with a full answer key and worked solutions. A matrix is a grid of numbers. For a 2×2 matrix [[a, b], [c, d]], the determinant is ad − bc.
Free
Foundation
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with matrix multiplication techniques
Identify working with matrix multiplication techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with matrix multiplication techniques
Explain working with matrix multiplication techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with matrix multiplication techniques
Calculate working with matrix multiplication techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with matrix multiplication techniques
Compare working with matrix multiplication techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Working with Matrix Multiplication Techniques works
A matrix is a grid of numbers. For a 2×2 matrix [[a, b], [c, d]], the determinant is ad − bc.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Find the determinant of [[6, 1], [3, 0]].[1]
- 2.Find the determinant of [[2, 4], [-3, 0]].[1]
- 3.Find the determinant of [[3, -2], [4, 6]].[1]
- 4.Find the determinant of [[-4, 6], [2, 6]].[1]
- 5.Find the determinant of [[1, 0], [1, 6]].[2]
- 6.Find the determinant of [[-1, 3], [1, -3]].[2]
- 7.Find the determinant of [[6, 6], [4, 0]].[2]
- 8.Find the determinant of [[5, 1], [5, 4]].[2]
- 9.Find the determinant of [[4, 5], [-4, 5]].[3]
- 10.Find the determinant of [[4, 5], [-2, 5]].[3]
- 11.Find the determinant of [[-1, 3], [4, 5]].[3]
- 12.Find the determinant of [[2, 3], [1, 3]].[3]
Show answers and working
1. -3
det = ad − bc. 6 × 0 − 1 × 3 = -3.
2. 12
det = ad − bc. 2 × 0 − 4 × -3 = 12.
3. 26
det = ad − bc. 3 × 6 − -2 × 4 = 26.
4. -36
det = ad − bc. -4 × 6 − 6 × 2 = -36.
5. 6
det = ad − bc. 1 × 6 − 0 × 1 = 6.
6. 0
det = ad − bc. -1 × -3 − 3 × 1 = 0.
7. -24
det = ad − bc. 6 × 0 − 6 × 4 = -24.
8. 15
det = ad − bc. 5 × 4 − 1 × 5 = 15.
9. 40
det = ad − bc. 4 × 5 − 5 × -4 = 40.
10. 30
det = ad − bc. 4 × 5 − 5 × -2 = 30.
11. -17
det = ad − bc. -1 × 5 − 3 × 4 = -17.
12. 3
det = ad − bc. 2 × 3 − 3 × 1 = 3.
Worked examples
Find the determinant of [[2, -2], [-3, -3]].
- det = ad − bc.
- 2 × -3 − -2 × -3 = -12.
- Answer: -12
Find the determinant of [[2, 0], [1, -1]].
- det = ad − bc.
- 2 × -1 − 0 × 1 = -2.
- Answer: -2
Find the determinant of [[-4, 0], [-1, 3]].
- det = ad − bc.
- -4 × 3 − 0 × -1 = -12.
- Answer: -12
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Calculates ab − cd.
Correction: Multiply the diagonals: ad − bc.
Gets signs wrong with negatives.
Correction: Bracket negatives before multiplying.
Teacher tips
- · Colour the two diagonals in different colours.
Parent tips
- · Point out spreadsheets as grids of numbers.
Real-life applications
- · Computer graphics, transformations.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Working with Matrix Multiplication Techniques worksheet really free?
- Yes. Every worksheets on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Working with Matrix Multiplication Essentials, Introducing Matrix Multiplication. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Working with Matrix Multiplication Techniques?
- Move on to Working with Matrix Multiplication Word Problems, Working with Matrix Multiplication Common Errors, Introducing Matrix Multiplication, Matrix Multiplication in Context, which build directly on this idea.
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