Find the Inverse [[1,0,0],[0,1,0],[0,0,1]]

Problem

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

Solution

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

2. Apply the property of the identity matrix, which states that the identity matrix is its own inverse.

3. Verify the definition of an inverse matrix, where A⋅A(−1)=I

4. Conclude that since I⋅I=I the inverse of the identity matrix is the identity matrix itself.

Final Answer

[[1,0,0],[0,1,0],[0,0,1]](−1)=[[1,0,0],[0,1,0],[0,0,1]]

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