Multiply the Matrices

Problem

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

Solution

1. Identify the type of matrices being multiplied. Both are 3×3 diagonal matrices.

2. Apply the rule for multiplying diagonal matrices, which states that the product of two diagonal matrices is a diagonal matrix where each diagonal element is the product of the corresponding diagonal elements of the factors.

3. Calculate the first diagonal element: (−1)×(−1)=1

4. Calculate the second diagonal element: 2×2=4

5. Calculate the third diagonal element: 3×3=9

6. Construct the resulting matrix using these calculated values on the main diagonal and zeros elsewhere.

Final Answer

[[−1,0,0],[0,2,0],[0,0,3]]*[[−1,0,0],[0,2,0],[0,0,3]]=[[1,0,0],[0,4,0],[0,0,9]]

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