JAMB 2012 Mathematics · Question 29

Given that I3 is a unit matrix of order 3, find |I3|

Options

A.-1
B.O
C.1
D.2

Answer: C. 1

Explanation written with AI and checked against the answer key

Analyze the question: I₃ is the 3×3 identity (unit) matrix. We are asked for its determinant, written |I₃|. Concept: The identity matrix has 1s on the main diagonal and 0s everywhere else. The determinant of a diagonal (or triangular) matrix is the product of its diagonal entries. Solution: I₃ = | 1 0 0 | | 0 1 0 | | 0 0 1 | Expand along the first row: |I₃| = 1 × (1·1 − 0·0) − 0 × (0·1 − 0·0) + 0 × (0·0 − 1·0) |I₃| = 1 × 1 − 0 + 0 = 1 You can also see it from the diagonal product: 1 × 1 × 1 = 1. Answer: The determinant of any identity matrix, of any order, is 1. The correct option is C. Tip: Remember that |Iₙ| = 1 for every n. Don't confuse it with the zero matrix, whose determinant is 0. When you see "unit matrix" in JAMB, think "identity", and the determinant is always 1.

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