Find the Determinant det [[2,1],[1,2]]^-1

Problem

det(2)

Solution

1. Identify the matrix A and the property of determinants for inverse matrices.

A=[[2,1],[1,2]]

2. Apply the property that the determinant of an inverse matrix is the reciprocal of the determinant of the original matrix.

det(A(−1))=1/det(A)

3. Calculate the determinant of the 2×2 matrix A using the formula a*d−b*c

det(A)=(2)*(2)−(1)*(1)

4. Simplify the result of the subtraction.

det(A)=4−1

det(A)=3

5. Substitute the value of det(A) back into the reciprocal formula.

det(A(−1))=1/3

Final Answer

det(2)=1/3

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