What is the determinant of the matrix [[0, 1], [1, 0]]?

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Question: What is the determinant of the matrix [[0, 1], [1, 0]]?

Options:

Correct Answer: -1

Solution:

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

What is the determinant of the matrix [[0, 1], [1, 0]]?

What is the determinant of the matrix [[0, 1], [1, 0]]?

Step 1: Identify the matrix. The matrix is [[0, 1], [1, 0]].
Step 2: Write down the formula for the determinant of a 2x2 matrix. The formula is (a*d) - (b*c), where the matrix is [[a, b], [c, d]].
Step 3: Assign the values from the matrix to the variables: a = 0, b = 1, c = 1, d = 0.
Step 4: Substitute the values into the formula: (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.
Step 8: The result is -1, which is the determinant of the matrix.

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