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

Problem

p=[[−1,−1],[−2,−1]]

Solution

1. Identify the matrix p as a 2×2 matrix of the form [[a,b],[c,d]] where a=−1 b=−1 c=−2 and d=−1

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

det(p)=(−1)*(−1)−(−1)*(−2)

det(p)=1−2

det(p)=−1

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

p(−1)=1/(−1)*[[−1,−(−1)],[−(−2),−1]]

4. Simplify the scalar multiplication and the signs within the matrix.

p(−1)=−1*[[−1,1],[2,−1]]

p(−1)=[[1,−1],[−2,1]]

Final Answer

p(−1)=[[1,−1],[−2,1]]

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