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

Problem

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

Solution

1. Identify the given matrix as the 2×2 identity matrix, denoted as I

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

3. Verify using the formula for the inverse of a 2×2 matrix A=[[a,b],[c,d]] where A(−1)=1/(a*d−b*c)*[[d,−b],[−c,a]]

4. Calculate the determinant a*d−b*c=(1)*(1)−(0)*(0)=1

5. Apply the formula to find the inverse matrix.

A(−1)=1/1*[[1,0],[0,1]]

6. Simplify the resulting matrix.

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

Final Answer

[[1,0],[0,1]](−1)=[[1,0],[0,1]]

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