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

Practice Questions

Q1
What is the determinant of the identity matrix I = [[1, 0], [0, 1]]? (2021)
  1. 0
  2. 1
  3. -1
  4. 2

Questions & Step-by-Step Solutions

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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