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

Problem

[[2,3],[1,1]](−1)

Solution

1. Identify the matrix A and the formula for the inverse of a 2×2 matrix.

A=[[a,b],[c,d]]=[[2,3],[1,1]]

A(−1)=1/(a*d−b*c)*[[d,−b],[−c,a]]

2. Calculate the determinant of the matrix, which is a*d−b*c

det(A)=(2)*(1)−(3)*(1)

det(A)=2−3

det(A)=−1

3. Swap the elements on the main diagonal and change the signs of the elements on the off-diagonal.

[[d,−b],[−c,a]]=[[1,−3],[−1,2]]

4. Multiply the resulting matrix by the reciprocal of the determinant.

A(−1)=1/(−1)*[[1,−3],[−1,2]]

A(−1)=[[−1,3],[1,−2]]

Final Answer

[[2,3],[1,1]](−1)=[[−1,3],[1,−2]]

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