Find the Inverse [[3,1],[5,2]]

Problem

[[3,1],[5,2]]

Solution

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

A=[[3,1],[5,2]]

a=3,b=1,c=5,d=2

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

det(A)=(3)*(2)−(1)*(5)

det(A)=6−5

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,−1],[−5,3]]

4. Simplify the expression by multiplying the scalar into the matrix.

A(−1)=[[2,−1],[−5,3]]

Final Answer

[[3,1],[5,2]](−1)=[[2,−1],[−5,3]]

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