Multiply the Matrices

Problem

[[1,0,0],[0,1,0],[0,0,1]]*[[2,5,4],[1,3,2],[3,6,0]]

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. Verify the multiplication by calculating the dot product of the first row of the identity matrix [1,0,0] and the first column of the second matrix [2,1,3]T

1*(2)+0*(1)+0*(3)=2

4. Conclude that since multiplying any matrix by the identity matrix leaves the matrix unchanged, the result is the second matrix itself.

Final Answer

[[1,0,0],[0,1,0],[0,0,1]]*[[2,5,4],[1,3,2],[3,6,0]]=[[2,5,4],[1,3,2],[3,6,0]]

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