Find the Inverse [[-1,1],[1,-2]]

Problem

[[−1,1],[1,−2]]

Solution

1. Identify the matrix A and its elements.

A=[[a,b],[c,d]]=[[−1,1],[1,−2]]

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

det(A)=(−1)*(−2)−(1)*(1)

det(A)=2−1

det(A)=1

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

A(−1)=1/1*[[−2,−1],[−1,−1]]

4. Simplify the expression by multiplying the scalar through the matrix.

A(−1)=[[−2,−1],[−1,−1]]

Final Answer

[[−1,1],[1,−2]](−1)=[[−2,−1],[−1,−1]]

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