Exams › JEE Main › Maths

If A and B are matrices of the same order, then the matrix expression AB^T - BA^T is a

1. skew symmetric matrix
2. zero matrix
3. symmetric matrix
4. identity matrix

Correct answer: skew symmetric matrix

Solution

Transposing: (AB^T-BA^T)^T = (AB^T)^T-(BA^T)^T = BA^T-AB^T = -(AB^T-BA^T). A matrix equal to the negative of its transpose is skew-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 →