Matrices and Determinants: JAMB Mathematics Questions, Answers & Notes

What Matrices and Determinants covers in the JAMB Mathematics syllabus

A matrix is a rectangular array of numbers; its order is rows × columns. Add or subtract matrices of the same order entry by entry, and scalar-multiply by multiplying every entry. For a 2×2 matrix [[a,b],[c,d]], the determinant is ad − bc; a matrix with determinant 0 is singular (no inverse). The identity matrix I has 1s on the leading diagonal and 0s elsewhere, and multiplying by I leaves a matrix unchanged. Matrix multiplication is defined only when the inner dimensions match, and the result takes the outer dimensions. The transpose swaps rows and columns.

For Matrices and Determinants, JAMB expects you to be able to:

• Add, subtract and scalar-multiply matrices
• Multiply matrices and find the determinant of a 2×2 matrix
• Recognise special matrices (identity, scalar, singular) and the transpose

Key facts & revision notes: Matrices and Determinants

These are the recurring points our Matrices and Determinants questions test — revise them until each feels automatic, then practise the questions above to lock them in.

• For a 2×2 matrix [[a,b],[c,d]], determinant = ad − bc = (2×4) − (1×3) = 8 − 3 = 5.
• Add corresponding entries: [[1+5,2+6],[3+7,4+8]] = [[6,8],[10,12]].
• A diagonal matrix with equal diagonal entries (and zeros elsewhere) is a scalar matrix.
• Scalar multiplication multiplies every entry by 2: [[2,4],[6,8]].
• (5×1) − (2×3) = 5 − 6 = −1.
• A matrix whose determinant is zero is called a singular matrix (it has no inverse).
• Subtract corresponding entries: [[10−4,10−5],[10−6,10−7]] = [[6,5],[4,3]].
• This matrix has 2 rows and 3 columns, so 2×3.
• Determinant = 4x − 6 = 10, so 4x = 16, x = 4.
• The identity matrix has 1s on the leading diagonal and 0s elsewhere: [[1,0],[0,1]].
• Multiplying by the identity matrix leaves the other matrix unchanged.
• AB = (2×4) + (3×5) = 8 + 15 = 23, a 1×1 matrix [23].
• The transpose swaps rows and columns: row 1 (1,2) becomes column 1, giving [[1,3],[2,4]].
• (6×2) − (4×3) = 12 − 12 = 0 (a singular matrix).
• Multiplying by the scalar matrix 2I doubles every entry: [[6,8],[10,12]].
• A row matrix consists of a single row of entries.
• Swapping two rows of a matrix changes the sign of the determinant, giving −D.
• Singular means determinant = 0: 2x − 4 = 0, so x = 2.
• Adding the zero matrix changes nothing, so the result is the original matrix.
• AB is defined when inner dimensions match (3=3); the result has the outer dimensions 2×2.
• det = (3×4) − (2×1) = 12 − 2 = 10.
• Add corresponding entries.
• (4×1) − (3×2) = 4 − 6 = −2.
• Multiply every entry by 3.

Worked examples

Three Matrices and Determinants questions with the answer and a short explanation, so you can see how the topic is set before you practise the full set.

How Matrices and Determinants is tested in JAMB Mathematics

Our Matrices and Determinants bank holds 40 questions (16 easy, 18 medium, 6 hard). JAMB Mathematics typically returns to Matrices and Determinants year after year, so steady practice on this topic is high-value revision. Questions are multiple-choice with four options, and at UTME pace you get roughly 40 seconds each — which is why timed practice matters.

How to answer Matrices and Determinants questions

Work the stem first and predict the answer before you look at the options; then eliminate the ones that contradict the key facts above. Watch for “which is not…”, “all of the above” and “except” style stems, which are where rushed candidates lose easy marks on Matrices and Determinants. If a calculation or a precise definition is involved, work it from first principles rather than guessing from a half-remembered rule. When two options look right, re-read the stem for the qualifier that separates them — JAMB rarely repeats an option by accident. If you are still unsure, eliminate the two weakest choices to lift your odds, flag the question, and move on; never burn a full minute on one Mathematics item when the exam gives you about forty seconds each. Then come back to flagged questions with whatever time remains. The single most reliable way to get faster at Matrices and Determinants is repeated timed practice, so use the button above until the recurring patterns feel automatic.

Common mistakes to avoid in Matrices and Determinants

The errors that cost marks on Matrices and Determinants are usually careless rather than conceptual: misreading a negative stem, confusing two similar terms, or rushing a definition you actually know. Candidates also over-rely on “expo” and last-minute cramming instead of understanding the topic — which fails the moment JAMB rephrases a familiar idea. Treat every option as a claim to be checked against the facts above, keep your working tidy for any calculation, and don’t change a considered answer on a hunch. Above all, revise Matrices and Determinants actively by answering questions, not just by re-reading notes — recall under time is what the exam rewards.

Frequently asked questions

Is Matrices and Determinants part of the JAMB Mathematics syllabus?

Yes. Matrices and Determinants is a recognised topic in the JAMB Mathematics syllabus, covering add, subtract and scalar-multiply matrices. You should be able to recall its key facts and apply them to multiple-choice questions.

How many Matrices and Determinants questions can I practise on Belmadeng?

There are 40 original, JAMB-standard Matrices and Determinants questions in our free bank, each with the correct answer and a worked explanation. You can practise them untimed or as a timed test.

What are the most important points to know about Matrices and Determinants?

A matrix is a rectangular array of numbers; its order is rows × columns. Add or subtract matrices of the same order entry by entry, and scalar-multiply by multiplying every entry. For a 2×2 matrix [[a,b],[c,d]], the determinant is ad − bc; a matrix with determinant 0 is singular (no inverse). The id…

How do I answer Matrices and Determinants questions quickly in JAMB?

Read the stem carefully, eliminate clearly wrong options, and match the remaining choices to the key facts for Matrices and Determinants. Practising timed Matrices and Determinants questions builds the speed you need for UTME's pace of about 40 seconds per question.

Are these JAMB Mathematics Matrices and Determinants questions past questions or original?

They are original questions written to JAMB (UTME) standard and mapped to the official syllabus — not reproduced past papers. This keeps them legal to use freely while closely mirroring how the real exam tests the topic.

Where can I practise Matrices and Determinants questions free without signing up?

Right here — tap “Start Matrices and Determinants practice” on this page to begin instantly. Belmadeng's CBT practice is completely free and needs no sign-up, download or subscription.

About these questions: original, JAMB-standard items written from the official UTME Mathematics syllabus (last reviewed 2026-09-18). Belmadeng is an independent study platform and is not affiliated with JAMB. Spotted an error? Use the report link.