Find the Inverse [[8,0],[729,64]]

Problem

[[8,0],[729,64]]

Solution

1. Identify the matrix A and its elements.

A=[[a,b],[c,d]]=[[8,0],[729,64]]

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

det(A)=(8)*(64)−(0)*(729)

det(A)=512

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

A(−1)=1/512*[[64,0],[−729,8]]

4. Distribute the scalar 1/512 to each element inside the matrix.

A(−1)=[[64/512,0/512],[(−729)/512,8/512]]

5. Simplify the fractions to their lowest terms.

A(−1)=[[1/8,0],[−729/512,1/64]]

Final Answer

[[8,0],[729,64]](−1)=[[1/8,0],[−729/512,1/64]]

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