Exams › JEE Advanced › Maths

Given the 3x3 matrix A = [[x, 2, -1], [-1, 1, 2], [2, -1, 1]] with x != -25/3, and det(adj(adj(A))) = 14⁴, find the value(s) of x and/or det(2A).

1. x = 1
2. det(2A) = 112
3. x = 2
4. det(2A) = 256

Correct answer: x = 1

Solution

For a 3x3 matrix, det(adj(adj A)) = det(A)⁴. Setting det(A)⁴ = 14⁴ gives det(A) = 14. Computing det(A) = 3x + 11 = 14 yields x = 1. Then det(2A) = 2³ * det(A) = 8 * 14 = 112. Correct options: A (x=1) and B (det(2A)=112).

Related JEE Advanced Maths questions

• Given that A and B are symmetric matrices and they commute (AB = BA), what type of matrix is A^T B?
• Given two matrices A and B satisfying AB = B and BA = A, what is the value of A² + B²?
• Consider the matrix P = [1, 0, 0; 4, 1, 0; 16, 4, 1] and the identity matrix I of size 3. If a matrix Q = [q_(ij)] satisfies P⁵⁰ - Q = I, what is the value of (q₃₁ + q₃₂)/(q₂₁) ?
• Which of the following matrices cannot be expressed as the square of a 3 × 3 matrix with real elements?
• What is the total number of 3 × 3 matrices M, whose elements are chosen from {0, 1, 2}, such that the sum of the diagonal elements of MᵀM equals 5?
• Given the matrix M = [[5/2, 3/2], [−3/2, −1/2]], which of the following represents the value of M raised to the power 2022?

⚔️ Practice JEE Advanced Maths free + battle 1v1 →