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JAMB Mathematics 2012 Paper

Question : 22

Total: 48

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

Solution:

Concept:

A unit matrix (identity matrix) has 1 on its main diagonal and 0 elsewhere. Its determinant is always 1.

Explanation:

For order 3, the identity matrix is:

I_3 = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}

Expand the determinant along the first row:

|I_3| = 1 \begin{vmatrix} 1 & 0 \\ 0 & 1 \end{vmatrix} - 0 \begin{vmatrix} 0 & 0 \\ 0 & 1 \end{vmatrix} + 0 \begin{vmatrix} 0 & 1 \\ 0 & 0 \end{vmatrix}

The terms multiplied by 0 all vanish, leaving:

|I_3| = 1(1 \cdot 1 - 0 \cdot 0) = 1(1) = 1

Answer:

|I_3| = 1

, so the correct option is C.

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