Find the Inverse [[3,2],[7,5]]

Problem

[[3,2],[7,5]]

Solution

1. Identify the matrix A and its elements a=3 b=2 c=7 and d=5

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

det(A)=(3)*(5)−(2)*(7)

det(A)=15−14

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*[[5,−2],[−7,3]]

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

A(−1)=[[5,−2],[−7,3]]

Final Answer

[[3,2],[7,5]](−1)=[[5,−2],[−7,3]]

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