If \( E = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \), what is \( |E

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Question: If \\( E = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix} \\), what is \\( |E| \\)? (2023)

Options:

Correct Answer: -1

Exam Year: 2023

Solution:

The determinant is calculated as \\( 0*0 - 1*1 = 0 - 1 = -1 \\).

If \( E = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \), what is \( |E| \)? (2023)

If \( E = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \), what is \( |E| \)? (2023)

Step 1: Identify the matrix E, which is given as E = [[0, 1], [1, 0]].
Step 2: Recall the formula for the determinant of a 2x2 matrix, which is |A| = ad - bc, where A = [[a, b], [c, d]].
Step 3: Assign the values from matrix E to the variables: a = 0, b = 1, c = 1, d = 0.
Step 4: Substitute the values into the determinant formula: |E| = (0 * 0) - (1 * 1).
Step 5: Calculate the first part: 0 * 0 = 0.
Step 6: Calculate the second part: 1 * 1 = 1.
Step 7: Subtract the second part from the first part: 0 - 1 = -1.
Step 8: Conclude that the determinant |E| is -1.

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