Find the Determinant ay-pr=1[[a,p],[r,y]]^-1

Problem

det([[a,p],[r,y]](−1))

Solution

1. Identify the matrix A and its given condition.

A=[[a,p],[r,y]]

det(A)=a*y−p*r

2. Apply the given constraint a*y−p*r=1

det(A)=1

3. Use the property of determinants for inverse matrices, which states that the determinant of the inverse is the reciprocal of the determinant of the original matrix.

det(A(−1))=1/det(A)

4. Substitute the value of det(A) into the formula.

det(A(−1))=1/1

det(A(−1))=1

Final Answer

det([[a,p],[r,y]](−1))=1

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