Find the Inverse [[1,-1],[1,1]]

Problem

[[1,−1],[1,1]]

Solution

1. Identify the matrix A and its elements.

A=[[a,b],[c,d]]=[[1,−1],[1,1]]

2. Calculate the determinant of the matrix using the formula det(A)=a*d−b*c

det(A)=(1)*(1)−(−1)*(1)

det(A)=1+1=2

3. Apply the inverse formula for a 2×2 matrix, which is A(−1)=1/det(A)*[[d,−b],[−c,a]]

A(−1)=1/2*[[1,1],[−1,1]]

4. Distribute the scalar 1/2 to each element inside the matrix.

A(−1)=[[1/2,1/2],[−1/2,1/2]]

Final Answer

[[1,−1],[1,1]](−1)=[[1/2,1/2],[−1/2,1/2]]

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