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If A = [[1, 0], [0, 1]] and B = [[2, 3], [4, 5]], what is AB?

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Question: If A = [[1, 0], [0, 1]] and B = [[2, 3], [4, 5]], what is AB?

Options:

  1. [2, 3], [4, 5]
  2. [1, 0], [0, 1]
  3. [0, 0], [0, 0]
  4. [6, 8], [12, 15]

Correct Answer: [2, 3], [4, 5]

Solution: 

AB = [[1*2 + 0*4, 1*3 + 0*5], [0*2 + 1*4, 0*3 + 1*5]] = [[2, 3], [4, 5]].

If A = [[1, 0], [0, 1]] and B = [[2, 3], [4, 5]], what is AB?

Practice Questions

Q1
If A = [[1, 0], [0, 1]] and B = [[2, 3], [4, 5]], what is AB?
  1. [2, 3], [4, 5]
  2. [1, 0], [0, 1]
  3. [0, 0], [0, 0]
  4. [6, 8], [12, 15]

Questions & Step-by-Step Solutions

If A = [[1, 0], [0, 1]] and B = [[2, 3], [4, 5]], what is AB?
Correct Answer: [[2, 3], [4, 5]]
  • Step 1: Identify the matrices A and B. A = [[1, 0], [0, 1]] and B = [[2, 3], [4, 5]].
  • Step 2: Understand that to multiply two matrices, we take rows from the first matrix (A) and columns from the second matrix (B).
  • Step 3: For the first element of the resulting matrix AB, take the first row of A and the first column of B: (1*2 + 0*4). This equals 2.
  • Step 4: For the second element of the first row of AB, take the first row of A and the second column of B: (1*3 + 0*5). This equals 3.
  • Step 5: For the first element of the second row of AB, take the second row of A and the first column of B: (0*2 + 1*4). This equals 4.
  • Step 6: For the second element of the second row of AB, take the second row of A and the second column of B: (0*3 + 1*5). This equals 5.
  • Step 7: Combine all the results into the final matrix AB: [[2, 3], [4, 5]].
  • Matrix Multiplication – The process of multiplying two matrices by taking the dot product of rows and columns.
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