Matrices · Form 5
Matrices: Common Mistakes
The mistakes that quietly cost marks in Matrices, and how to avoid each one in the SPM exam.
In our experience teaching Matrices, most lost marks come from a small set of repeated slips, not from a lack of understanding. Here they are, with the fix for each.
Mistakes to avoid
- Multiplying matrices in the wrong order (order matters)
- Sign errors in the inverse formula
- Trying to invert a matrix whose determinant is zero
Six more slips that quietly cost marks
- What students write: for M = [[4,3],[2,5]] they put M⁻¹ = (1/14)[[4,-3],[-2,5]]. → Why it loses marks: they negated b and c but forgot to SWAP the diagonal 4 and 5. → Correct working: swap first, then negate: M⁻¹ = (1/14)[[5,-3],[-2,4]].
- What students write: solving AX = B, they compute X = BA⁻¹. → Why it loses marks: order matters, and B on the left does not even conform for a 2×1 B. → Correct working: multiply on the LEFT, X = A⁻¹B.
- What students write: 3 × [[1,2],[4,5]] = [[3,2],[4,5]]. → Why it loses marks: scalar multiplication must reach every entry, not just the top-left. → Correct working: 3 × [[1,2],[4,5]] = [[3,6],[12,15]].
- What students write: [[1,2],[3,4]] × [[5,6],[7,8]] = [[5,12],[21,32]]. → Why it loses marks: that is element-by-element, not matrix multiplication. → Correct working: row into column: [[1·5+2·7, 1·6+2·8],[3·5+4·7, 3·6+4·8]] = [[19,22],[43,50]].
- What students write: determinant of [[4,3],[2,5]] = 4·5 + 3·2 = 26. → Why it loses marks: the determinant is ad − bc, a subtraction, not a sum. → Correct working: 4·5 − 3·2 = 20 − 6 = 14.
- What students write: asked for the final numeric inverse, they leave it as (1/14)[[5,-3],[-2,4]]. → Why it loses marks: the fraction must be shared into every entry for the final form. → Correct working: (1/14)[[5,-3],[-2,4]] = [[5/14, -3/14],[-1/7, 2/7]].
The one slip to guard against above all
Notice that most of the six errors above corrupt not one number but every value that follows. That is what makes the inverse the danger zone of this chapter: a matrix built once and reused three times.
Get the swap, the negatives and the multiplication order right on that single line, and the rest of the question tends to fall into place.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Which single mistake in this chapter costs the most marks?
Multiplying in the wrong order when solving AX = B, writing X = BA⁻¹ instead of X = A⁻¹B. Because the inverse must sit on the left of B, getting this wrong makes the whole final answer incorrect even if every earlier line was perfect, so it typically loses the most marks in one stroke.
If I compute the determinant wrongly, do I lose every mark in that part?
Usually not all of them. SPM marking often gives follow-through marks: if your method is right and only the determinant value is wrong, later steps that correctly use that wrong value can still earn method marks.
You lose the accuracy mark, so show every step clearly rather than jumping to the final matrix.
How do I stop making sign errors in the inverse?
Write the adjusted matrix first, separately: swap the diagonal, then negate the off-diagonal pair. Look at those four numbers on their own and check the two negatives are in the right places before you attach the 1/determinant.
Handling the pattern and the fraction in two clear stages removes most sign slips.