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Question
If I3 denotes identity matrix of order 3 × 3, write the value of its determinant.
Solution
In an identity matrix, all the diagonal elements are 1 and rest of the elements are 0.
Here,
\[I_3 = \begin{vmatrix} 1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1 \end{vmatrix}\]
\[ = 1 \times \begin{vmatrix} 1 & 0\\0 & 1 \end{vmatrix} \left[\text{ Expanding along }C_1 \right]\]
\[ = 1\]
\[ \Rightarrow I_3 = 1\]
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