Find the Inverse [[7,8],[4,6]]

Problem

[[7,8],[4,6]]

Solution

1. Identify the matrix A and its elements a=7 b=8 c=4 and d=6

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

det(A)=(7)*(6)−(8)*(4)

det(A)=42−32

det(A)=10

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

A(−1)=1/10*[[6,−8],[−4,7]]

4. Distribute the scalar 1/10 to each element inside the matrix.

A(−1)=[[6/10,(−8)/10],[(−4)/10,7/10]]

5. Simplify the fractions to their lowest terms.

A(−1)=[[3/5,−4/5],[−2/5,7/10]]

Final Answer

[[7,8],[4,6]](−1)=[[3/5,−4/5],[−2/5,7/10]]

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