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

1 question

1 item

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

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

Steps: 7

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]].