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

Mathematics

JAMB 2012

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

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

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Correct Answer: Option C

Explanation

Recall that a unit matrice is a diagonal matrix in which the elements in the leading diagonal is unity. Therefore,

I₃ = \(\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}\)

I₃ = \(+1\begin{vmatrix} 1 & 0 \\ 0 & 1 \end{vmatrix} - 0\begin{vmatrix} 0 & 0 \\ 0 & 1 \end{vmatrix} + 0 \begin{vmatrix} 0 & 1 \\ 0 & 0 \end{vmatrix} \)

I₃ = +1(1 - 0) - 0(0 - 0) + 0(0 - 0)

= 1(1)

= 1

There is an explanation video available below.

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