What is the determinant of the matrix \( H = \begin{pmatrix} 1 & 0 & 0 \

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Question: What is the determinant of the matrix \\( H = \\begin{pmatrix} 1 & 0 & 0 \\\\ 0 & 1 & 0 \\\\ 0 & 0 & 1 \\end{pmatrix} \\)? (2022)

Options:

Correct Answer: 1

Exam Year: 2022

Solution:

The determinant of the identity matrix is always 1.

What is the determinant of the matrix \( H = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \)? (2022)

What is the determinant of the matrix \( H = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \)? (2022)

Step 1: Identify the matrix H. The matrix H is given as H = [[1, 0, 0], [0, 1, 0], [0, 0, 1]].
Step 2: Recognize that this matrix is an identity matrix. An identity matrix has 1s on the diagonal and 0s elsewhere.
Step 3: Recall the property of the determinant of an identity matrix. The determinant of any identity matrix is always 1.
Step 4: Conclude that the determinant of the matrix H is 1.

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