What is the determinant of the identity matrix I = [[1, 0], [0, 1]]? (2021)

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Question: What is the determinant of the identity matrix I = [[1, 0], [0, 1]]? (2021)

Options:

Correct Answer: 1

Solution:

Det(I) = (1*1) - (0*0) = 1 - 0 = 1.

What is the determinant of the identity matrix I = [[1, 0], [0, 1]]? (2021)

What is the determinant of the identity matrix I = [[1, 0], [0, 1]]? (2021)

Step 1: Identify the identity matrix I, which is [[1, 0], [0, 1]].
Step 2: Recall the formula for the determinant of a 2x2 matrix, which is Det(A) = (a*d) - (b*c), where A = [[a, b], [c, d]].
Step 3: In our identity matrix, a = 1, b = 0, c = 0, and d = 1.
Step 4: Substitute the values into the determinant formula: Det(I) = (1*1) - (0*0).
Step 5: Calculate the multiplication: 1*1 = 1 and 0*0 = 0.
Step 6: Subtract the results: 1 - 0 = 1.
Step 7: Conclude that the determinant of the identity matrix I is 1.

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