Multiply the Matrices [[1,2],[0,-1]]*[[1,0],[0,1]]

Problem

[[1,2],[0,−1]]*[[1,0],[0,1]]

Solution

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

2. Recognize that the second matrix is the identity matrix I Multiplying any matrix A by the identity matrix I results in the original matrix A

3. Calculate the top-left element by multiplying the first row of the first matrix by the first column of the second matrix: (1×1)+(2×0)=1

4. Calculate the top-right element by multiplying the first row of the first matrix by the second column of the second matrix: (1×0)+(2×1)=2

5. Calculate the bottom-left element by multiplying the second row of the first matrix by the first column of the second matrix: (0×1)+(−1×0)=0

6. Calculate the bottom-right element by multiplying the second row of the first matrix by the second column of the second matrix: (0×0)+(−1×1)=−1

Final Answer

[[1,2],[0,−1]]*[[1,0],[0,1]]=[[1,2],[0,−1]]

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