Find the Inverse [[1,2],[4,6]]

Problem

[[1,2],[4,6]]

Solution

1. Identify the matrix A and its elements a,b,c,d for the formula of a 2×2 inverse.

A=[[a,b],[c,d]]=[[1,2],[4,6]]

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

det(A)=(1)*(6)−(2)*(4)

det(A)=6−8=−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)*[[6,−2],[−4,1]]

4. Distribute the scalar 1/(−2) to each element inside the matrix to find the final values.

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

Final Answer

[[1,2],[4,6]](−1)=[[−3,1],[2,−0.5]]

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