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

Problem

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

Solution

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

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

det(A)=(1)*(5)−(2)*(3)

det(A)=5−6

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],[−3,1]]

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

A(−1)=[[−5,2],[3,−1]]

Final Answer

[[1,2],[3,5]](−1)=[[−5,2],[3,−1]]

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