Find the Inverse [[2,0],[0,2]]

Problem

[[2,0],[0,2]]

Solution

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

A=[[a,b],[c,d]]=[[2,0],[0,2]]

A(−1)=1/(a*d−b*c)*[[d,−b],[−c,a]]

2. Calculate the determinant of the matrix.

det(A)=(2)*(2)−(0)*(0)

det(A)=4

3. Apply the formula by swapping the diagonal elements and changing the signs of the off-diagonal elements.

A(−1)=1/4*[[2,0],[0,2]]

4. Scalar multiply each element of the matrix by the reciprocal of the determinant.

A(−1)=[[2/4,0/4],[0/4,2/4]]

5. Simplify the fractions.

A(−1)=[[1/2,0],[0,1/2]]

Final Answer

[[2,0],[0,2]](−1)=[[1/2,0],[0,1/2]]

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