Matrices & Determinants
Properties of determinants
Grade Class 12
Question:
If A, B and C are n x n matrices and det(A) = 2, det(B) = 3 and det(C) = 5, then the value of the det(A<sup>2</sup> BC<sup>-1</sup>) is equal to
Step-by-Step Solution
Key Concept: Use the properties of determinants: det(AB) = det(A)det(B), det(A^n) = (det(A))^n, and det(A^-1) = 1/det(A).
Given det(A) = 2, det(B) = 3, det(C) = 5. We need to find det(A<sup>2</sup> BC<sup>-1</sup>). Using properties of determinants: det(A<sup>2</sup> BC<sup>-1</sup>) = det(A<sup>2</sup>) * det(B) * det(C<sup>-1</sup>) = (det(A))<sup>2</sup> * det(B) * (1/det(C)) = (2)<sup>2</sup> * 3 * (1/5) = 4 * 3 / 5 = 12/5.
Correct Answer: 2