Both matrices
Write the 2×2 matrix for each transformation described.
AQA 8365 · 5.1–5.4 · Matrix composition
Composing transformations: which matrix goes on the right
The order mark. The matrix for the transformation applied FIRST sits on the right of the product, and reversing that gives a different transformation rather than an arithmetic error.
Reviewed family · Studara-authored items · No grade-uplift claim
The lost mark
One answer. Several places the method can fail.
Studara does not reduce the response to right or wrong. The reviewed contract checks these states independently.
Correct order
Place the matrix acting first on the RIGHT of the product.
Multiply and identify
Carry out the multiplication and name the single transformation it represents.
Why it goes wrong
The diagnosis stays uncertainty-safe.
A wrong response can support a specific measured diagnosis. A blind multiple-choice diagnostic records only a possible cause until later working provides stronger evidence.
01
The error
Multiplying in reading order — writing AB because A was described first, when applying A first means the product is BA.
02
Why it survives revision
The multiplication is still performed correctly and still yields a valid 2×2 matrix describing a real transformation. There is no arithmetic tell at all: the answer is well-formed, just the wrong transformation.
The worked repair
Repair the smallest broken step.
Teaching is not evidence. This one move is the repair; the proof checks begin after it disappears.
Write down which transformation acts on the vector first. That matrix goes immediately to the left of the vector — so, on the right of the product.
What happens after the repair
Correction is the start, not the result.
Immediate
Asked again straight away, on a different question
The repair leaves the screen and a new authored item checks the method unassisted. Being taught something is never evidence that it was learned, so this is the first stage that counts at all.
Delayed
Asked again after at least 1 day
A parallel form of the same method, unassisted, with the repair no longer on screen. A retest in the same session does not count.
Transfer
Asked again when the surface changes
The transfer form gives the product and asks which single transformation it represents, so the order has to be reasoned about rather than reproduced.
Exam
Asked again under exam conditions
Timed, carrying the mark tariff, in an exam-like response format and aligned to the specification. Any one of those missing and the evidence is refused.
REVIEWED BOUNDARY
This page covers one reviewed family: 5.1–5.4 · Matrix composition. Build both transformation matrices, preserve the order they act, multiply exactly, and identify the resulting geometry. Other families within the same GCSE Further Maths topic are outside this reviewed journey, and Studara does not apply the proof label to material that has not been reviewed. No grade-uplift claim is made anywhere on this site.
Straight answers
Before you use this guide.
Which matrix goes first when combining transformations?
The one that acts on the vector first goes on the right of the product. If A is applied first and then B, the combined matrix is BA, not AB.
Does the order actually change the answer?
Yes. Matrix multiplication is not commutative, so the reversed order gives a valid but different transformation — which is why the error is hard to spot.
Does Studara guarantee a higher grade?
No. Studara has not run a controlled outcome study and publishes no grade-uplift claim. What has been measured, what is withheld, and the metric that failed its bar are all on the public evidence page.
Turn this method into evidence