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

Problem

[[2,3],[5,7]](−1)

Solution

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

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

det(A)=(2)*(7)−(3)*(5)

det(A)=14−15

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)*[[7,−3],[−5,2]]

4. Distribute the scalar −1 to each element inside the matrix.

A(−1)=[[−7,3],[5,−2]]

Final Answer

[[2,3],[5,7]](−1)=[[−7,3],[5,−2]]

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