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

Problem

[[−2,3],[1,−2]]

Solution

1. Identify the matrix A and its elements a,b,c,d from the form [[a,b],[c,d]]

A=[[−2,3],[1,−2]]

a=−2,b=3,c=1,d=−2

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

det(A)=(−2)*(−2)−(3)*(1)

det(A)=4−3

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,−3],[−1,−2]]

4. Simplify the resulting matrix by multiplying each element by the scalar 1/1

A(−1)=[[−2,−3],[−1,−2]]

Final Answer

[[−2,3],[1,−2]](−1)=[[−2,−3],[−1,−2]]

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