Find the Inverse [[3,-2],[1,-1]]

Problem

[[3,−2],[1,−1]]

Solution

1. Identify the matrix A and its elements a=3 b=−2 c=1 and d=−1

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

det(A)=(3)*(−1)−(−2)*(1)

det(A)=−3+2

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)*[[−1,2],[−1,3]]

4. Distribute the scalar −1 to each element inside the matrix.

A(−1)=[[1,−2],[1,−3]]

Final Answer

[[3,−2],[1,−1]](−1)=[[1,−2],[1,−3]]

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