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.
