Exams › JEE Main › Maths

If A is a square matrix, then the matrix product A A^T is a

1. skew-symmetric matrix
2. symmetric matrix
3. diagonal matrix
4. matrix not covered by the above choices

Correct answer: symmetric matrix

Solution

(A A^T)^T = (A^T)^T A^T = A A^T, so A A^T equals its own transpose and is therefore symmetric.

Related JEE Main Maths questions

• 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
• Let A = [1 0 0; 0 1 0; a b −1] and let I denote the 3 × 3 identity matrix. Then the value of A² + 2A⁴ + 4A⁶ is

⚔️ Practice JEE Main Maths free + battle 1v1 →