Multiply the Matrices [[2,3],[5,7]][[1,0],[0,1]]

Problem

[[2,3],[5,7]]*[[1,0],[0,1]]

Solution

1. Identify the second matrix as the 2×2 identity matrix, denoted as I

2. Apply the property of the identity matrix, which states that any matrix A multiplied by the identity matrix I results in the original matrix A

3. Verify the multiplication by calculating the dot product of the rows of the first matrix and the columns of the second matrix.

4. Calculate the top-left element: (2×1)+(3×0)=2

5. Calculate the top-right element: (2×0)+(3×1)=3

6. Calculate the bottom-left element: (5×1)+(7×0)=5

7. Calculate the bottom-right element: (5×0)+(7×1)=7

Final Answer

[[2,3],[5,7]]*[[1,0],[0,1]]=[[2,3],[5,7]]

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