Find the Inverse [[0,1/8],[1/14,9/112]]

Problem

[[0,1/8],[1/14,9/112]]

Solution

1. Identify the matrix A and the formula for the inverse of a 2×2 matrix.

A=[[a,b],[c,d]]=[[0,1/8],[1/14,9/112]]

A(−1)=1/(a*d−b*c)*[[d,−b],[−c,a]]

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

det(A)=(0)*(9/112)−(1/8)*(1/14)

det(A)=0−1/112

det(A)=−1/112

3. Find the reciprocal of the determinant.

1/det(A)=1/(−1/112)

1/det(A)=−112

4. Swap the main diagonal elements and negate the off-diagonal elements to form the adjugate matrix.

adj(A)=[[9/112,−1/8],[−1/14,0]]

5. Multiply the adjugate matrix by the reciprocal of the determinant.

A(−1)=−112*[[9/112,−1/8],[−1/14,0]]

A(−1)=[[−112*(9/112),−112*(−1/8)],[−112*(−1/14),−112*(0)]]

6. Simplify the resulting entries.

A(−1)=[[−9,14],[8,0]]

Final Answer

[[0,1/8],[1/14,9/112]](−1)=[[−9,14],[8,0]]

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