Find the Determinant

Problem

A=[[3√(,3),−3],[3,3√(,3)]]

Solution

1. Identify the formula for the determinant of a 2×2 matrix A=[[a,b],[c,d]] which is det(A)=a*d−b*c

2. Substitute the values from the given matrix into the formula where a=3√(,3) b=−3 c=3 and d=3√(,3)

det(A)=(3√(,3))*(3√(,3))−(−3)*(3)

3. Multiply the terms in the first product by squaring the coefficient and the radical.

(3√(,3))*(3√(,3))=9⋅3=27

4. Multiply the terms in the second product.

(−3)*(3)=−9

5. Subtract the results to find the final value.

det(A)=27−(−9)=27+9=36

Final Answer

det(3√(,3))=36

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