Multiply the Matrices

Problem

[[0,0,1],[1,0,0],[0,1,0]]*[[0,0,1],[1,0,0],[0,1,0]]

Solution

1. Identify the dimensions of the matrices. Both are 3×3 matrices, so the resulting matrix will also be 3×3

2. Calculate the first row of the product by multiplying the first row of the left matrix by each column of the right matrix.

(0)*(0)+(0)*(1)+(1)*(0)=0

(0)*(0)+(0)*(0)+(1)*(1)=1

(0)*(1)+(0)*(0)+(1)*(0)=0

3. Calculate the second row of the product by multiplying the second row of the left matrix by each column of the right matrix.

(1)*(0)+(0)*(1)+(0)*(0)=0

(1)*(0)+(0)*(0)+(0)*(1)=0

(1)*(1)+(0)*(0)+(0)*(0)=1

4. Calculate the third row of the product by multiplying the third row of the left matrix by each column of the right matrix.

(0)*(0)+(1)*(1)+(0)*(0)=1

(0)*(0)+(1)*(0)+(0)*(1)=0

(0)*(1)+(1)*(0)+(0)*(0)=0

5. Assemble the resulting values into the final matrix structure.

Final Answer

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

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