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

Problem

[[2,1],[3,2]]

Solution

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

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

A(−1)=1/(a*d−b*c)*[[d,−b],[−c,a]]

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

det(A)=(2)*(2)−(1)*(3)

det(A)=4−3=1

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

[[d,−b],[−c,a]]=[[2,−1],[−3,2]]

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

A(−1)=1/1*[[2,−1],[−3,2]]

A(−1)=[[2,−1],[−3,2]]

Final Answer

[[2,1],[3,2]](−1)=[[2,−1],[−3,2]]

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