Evaluate \( \begin{vmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{vmatrix} \)

1 question

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Q: Evaluate \( \begin{vmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{vmatrix} \)

Solution: The determinant of the identity matrix is 1.

Steps: 4

Step 1: Identify the matrix given in the question. It is a 3x3 matrix: \( \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \).
Step 2: Recognize that this matrix is called the identity matrix, which has 1s on the diagonal and 0s elsewhere.
Step 3: Recall the property of the determinant of the identity matrix. The determinant of any identity matrix is always 1.
Step 4: Therefore, conclude that the determinant of the given matrix is 1.