Calculate the determinant of \( D = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{

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Question: Calculate the determinant of \\( D = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix} \\). (2021)

Options:

Correct Answer: 1

Exam Year: 2021

Solution:

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

Calculate the determinant of \( D = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \). (2021)

Calculate the determinant of \( D = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \). (2021)

Step 1: Identify the matrix D, which is D = [[0, 1], [1, 0]].
Step 2: Recall the formula for the determinant of a 2x2 matrix, which is given by det(A) = ad - bc, where A = [[a, b], [c, d]].
Step 3: Assign the values from the matrix D to the variables: a = 0, b = 1, c = 1, d = 0.
Step 4: Substitute the values into the determinant formula: det(D) = (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 of matrix D is -1.

Determinant Calculation – Understanding how to compute the determinant of a 2x2 matrix using the formula det(A) = ad - bc.
Matrix Properties – Recognizing the properties of matrices, particularly the identity and permutation matrices.