Find the Inverse [[-2,5],[3,4]]

Problem

[[−2,5],[3,4]]

Solution

1. Identify the matrix A and its elements a=−2 b=5 c=3 and d=4

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

det(A)=(−2)*(4)−(5)*(3)

det(A)=−8−15

det(A)=−23

3. Apply the inverse formula for a 2×2 matrix, which is A(−1)=1/det(A)*[[d,−b],[−c,a]]

A(−1)=1/(−23)*[[4,−5],[−3,−2]]

4. Distribute the scalar 1/(−23) to each element inside the matrix.

A(−1)=[[−4/23,5/23],[3/23,2/23]]

Final Answer

[[−2,5],[3,4]](−1)=[[−4/23,5/23],[3/23,2/23]]

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