Find the Inverse [[8,6],[5,4]]

Problem

[[8,6],[5,4]]

Solution

1. Identify the matrix A and its elements a=8 b=6 c=5 and d=4

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

det(A)=(8)*(4)−(6)*(5)

det(A)=32−30

det(A)=2

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

A(−1)=1/2*[[4,−6],[−5,8]]

4. Distribute the scalar 1/2 to each element inside the matrix.

A(−1)=[[4/2,(−6)/2],[(−5)/2,8/2]]

5. Simplify the fractions to find the final entries of the inverse matrix.

A(−1)=[[2,−3],[−2.5,4]]

Final Answer

[[8,6],[5,4]](−1)=[[2,−3],[−2.5,4]]

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