Multiply the Matrices

Problem

[[1,0,0],[0,1,0],[0,0,1]]*[[2,0,6],[0,3,0],[0,0,3]]

Solution

1. Identify the first matrix as the 3×3 identity matrix, denoted as I

2. Apply the property of the identity matrix, which states that for any square matrix A of the same dimension, I*A=A

3. Perform the multiplication by multiplying each row of the first matrix by each column of the second matrix to verify.

4. Calculate the element at row 1, column 1: (1×2)+(0×0)+(0×0)=2

5. Calculate the element at row 1, column 3: (1×6)+(0×0)+(0×3)=6

6. Observe that since the first matrix is the identity matrix, the resulting matrix is identical to the second matrix.

Final Answer

[[1,0,0],[0,1,0],[0,0,1]]*[[2,0,6],[0,3,0],[0,0,3]]=[[2,0,6],[0,3,0],[0,0,3]]

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