Exams › JEE Main › Maths

Let P = [[3, −5],[7, −12]] and Q = [[12, −5],[7, −3]]. Which of the following is not true for the matrix (PQ)^(−1)?

1. nilpotent
2. idempotent
3. involutory
4. symmetric

Correct answer: nilpotent

Solution

det(P) = -1 and det(Q) = -1; computing PQ gives the identity matrix I = [[1,0],[0,1]], so (PQ)^-1 = I. The identity is idempotent (I^2 = I), involutory (I^2 = I), and symmetric, but it is never nilpotent. The property that does NOT hold is nilpotent.

Related JEE Main Maths questions

• If A is a square matrix, then the matrix product A A^T is a
• Let f(α)=[cosα, sinα; -sinα, cosα]. If α, β, and γ are the angles of a triangle, then the product f(α)f(β)f(γ) is equal to
• Let A, B, and C be n × n matrices. Which of the following statements is true?
• Given the matrix A_α = [cos α -sin α; sin α cos α], which of the following identities is true?
• Let A be a square matrix satisfying (A−2I)(A+I)=O. Then A−1 equals:
• A square matrix P obeys the relation P² = I - P, where I denotes the identity matrix. If Pⁿ = 5I - 8P, then the value of n is

⚔️ Practice JEE Main Maths free + battle 1v1 →