Given that I3 is a unit matrix of order 3 find ... - JAMB Mathematics 2012 Question
Given that I3 is a unit matrix of order 3, find |I3|
A
-1
B
O
C
1
D
2
correct option: c
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
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
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