Find the Inverse [[1,2],[2,3]]

Problem

[[1,2],[2,3]]

Solution

1. Identify the matrix A and its elements a=1 b=2 c=2 and d=3

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

det(A)=(1)*(3)−(2)*(2)

det(A)=3−4

det(A)=−1

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

A(−1)=1/(−1)*[[3,−2],[−2,1]]

4. Distribute the scalar −1 to each element inside the matrix.

A(−1)=[[−3,2],[2,−1]]

Final Answer

[[1,2],[2,3]](−1)=[[−3,2],[2,−1]]

Want more problems? Check here!