Find the Determinant [[5,0,0],[0,5,0],[0,0,5]]

Problem

det(5)

Solution

1. Identify the type of matrix. The given matrix is a diagonal matrix because all entries outside the main diagonal are zero.

2. Apply the property for the determinant of a diagonal matrix. The determinant of a diagonal matrix is the product of the entries on its main diagonal.

3. Calculate the product of the diagonal elements.

5⋅5⋅5=125

Final Answer

det(5)=125

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