[latex]
\[
\textbf{1. Determinant of Identity Matrix:}
\]
\[
\text{The determinant of an identity matrix is always 1.}
\]

\[
\textbf{Question: Calculate the determinant of the identity matrix } I \textbf{ of order } 3 \textbf{ (3×3 matrix).}
\]

\[
I = \begin{pmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{pmatrix}
\]

\[
\textbf{Step 1: Identify the matrix type.}
\]
\[
\text{The given matrix is an identity matrix of order 3. An identity matrix has 1’s on the diagonal and 0’s elsewhere.}
\]

\[
\textbf{Step 2: Use the determinant property of triangular matrices.}
\]
\[
\text{The determinant of a triangular matrix is the product of its diagonal elements.}
\]

\[
\textbf{Step 3: Compute the product of diagonal elements.}
\]
\[
\text{Diagonal elements of } I \text{ are } 1, 1, 1.
\]
\[
\text{Product of diagonal elements: } 1 \cdot 1 \cdot 1 = 1.
\]

\[
\textbf{Step 4: Conclusion.}
\]
\[
\text{The determinant of the identity matrix } I \text{ is } 1.
\]

\[
\textbf{Answer: } \det(I) = 1.
\]