Exams › JEE Main › Maths

For any square matrix A, which of the following expressions is skew-symmetric?

1. A + A^T
2. A - A^T
3. AA^T
4. A^T A - A

Correct answer: A - A^T

Solution

A matrix S is skew-symmetric if S^T=-S. For S=A-A^T, S^T=A^T-A=-(A-A^T)=-S, so A-A^T is always skew-symmetric (while A+A^T and AA^T are symmetric).

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 →