[latex] \[ \textbf{1. Determinant of Identity Matrix:} \] \[ \text{The determinant of an identity matrix is always 1.} \] \[ \textbf{Question: Calculate the determinant of the identity matrix } I \textbf{ of order } 3 \textbf{ (3×3 matrix).} \] \[ I = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \] \[ \textbf{Step 1: Identify the matrix type.} \] \[ \text{The given matrix is an identity matrix of order 3. An identity matrix has 1’s on the diagonal and 0’s elsewhere.} \] \[ \textbf{Step 2: Use the determinant property of triangular matrices.} \] \[ \text{The determinant of a triangular matrix is the product of its diagonal elements.} \] \[ \textbf{Step 3: Compute the product of diagonal elements.} \] \[ \text{Diagonal elements of } I \text{ are } 1, 1, 1. \] \[ \text{Product of diagonal elements: } 1 \cdot 1 \cdot 1 = 1. \] \[ \textbf{Step 4: Conclusion.} \] \[ \text{The determinant of the identity matrix } I \text{ is } 1. \] \[ \textbf{Answer: } \det(I) = 1. \]