Multiply the Matrices [[0,1],[1,0]]*[[1,0],[0,-1]]

Problem

[[0,1],[1,0]]*[[1,0],[0,−1]]

Solution

1. Identify the dimensions of the matrices. Both are 2×2 matrices, so the resulting matrix will also be 2×2

2. Calculate the element in the first row, first column by taking the dot product of the first row of the first matrix and the first column of the second matrix: (0×1)+(1×0)=0

3. Calculate the element in the first row, second column by taking the dot product of the first row of the first matrix and the second column of the second matrix: (0×0)+(1×−1)=−1

4. Calculate the element in the second row, first column by taking the dot product of the second row of the first matrix and the first column of the second matrix: (1×1)+(0×0)=1

5. Calculate the element in the second row, second column by taking the dot product of the second row of the first matrix and the second column of the second matrix: (1×0)+(0×−1)=0

6. Assemble the resulting values into the final matrix.

Final Answer

[[0,1],[1,0]]*[[1,0],[0,−1]]=[[0,−1],[1,0]]

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