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

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

Options:

Correct Answer: 1

Solution:

The determinant of the identity matrix is 1.

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

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

Correct Answer: 1

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.

Determinants – Understanding how to calculate the determinant of a matrix, particularly the identity matrix.
Identity Matrix – Recognizing that the determinant of an identity matrix is always 1.