Find the Inverse [[2,4],[6,8]]

Problem

[[2,4],[6,8]]

Solution

1. Identify the matrix A and its elements a=2 b=4 c=6 and d=8

A=[[2,4],[6,8]]

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

det(A)=(2)*(8)−(4)*(6)

det(A)=16−24

det(A)=−8

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

A(−1)=1/(−8)*[[8,−4],[−6,2]]

4. Distribute the scalar 1/(−8) to each element inside the matrix.

A(−1)=[[8/(−8),(−4)/(−8)],[(−6)/(−8),2/(−8)]]

5. Simplify the resulting fractions to find the final inverse matrix.

A(−1)=[[−1,1/2],[3/4,−1/4]]

Final Answer

[[2,4],[6,8]](−1)=[[−1,1/2],[3/4,−1/4]]

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