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For the matrix J = [[0, 1], [1, 0]], what is J^2?

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Question: For the matrix J = [[0, 1], [1, 0]], what is J^2?

Options:

  1. [[1, 0], [0, 1]]
  2. [[0, 1], [1, 0]]
  3. [[0, 0], [0, 0]]
  4. [[1, 1], [1, 1]]

Correct Answer: [[1, 0], [0, 1]]

Solution: 

Calculating J^2 gives [[0, 1], [1, 0]] * [[0, 1], [1, 0]] = [[1, 0], [0, 1]], which is the identity matrix.

For the matrix J = [[0, 1], [1, 0]], what is J^2?

Practice Questions

Q1
For the matrix J = [[0, 1], [1, 0]], what is J^2?
  1. [[1, 0], [0, 1]]
  2. [[0, 1], [1, 0]]
  3. [[0, 0], [0, 0]]
  4. [[1, 1], [1, 1]]

Questions & Step-by-Step Solutions

For the matrix J = [[0, 1], [1, 0]], what is J^2?
  • Step 1: Identify the matrix J, which is [[0, 1], [1, 0]].
  • Step 2: To find J^2, we need to multiply J by itself: J * J.
  • Step 3: Write down the multiplication: [[0, 1], [1, 0]] * [[0, 1], [1, 0]].
  • Step 4: Calculate the first element of the resulting matrix: (0*0 + 1*1) = 1.
  • Step 5: Calculate the second element of the first row: (0*1 + 1*0) = 0.
  • Step 6: Calculate the first element of the second row: (1*0 + 0*1) = 0.
  • Step 7: Calculate the second element of the second row: (1*1 + 0*0) = 1.
  • Step 8: Combine the results to form the new matrix: [[1, 0], [0, 1]].
  • Step 9: Recognize that [[1, 0], [0, 1]] is the identity matrix.
  • Matrix Multiplication – Understanding how to multiply matrices, particularly 2x2 matrices.
  • Identity Matrix – Recognizing the identity matrix and its properties in matrix operations.
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