Exams › JEE Main › Maths

Let A, B, and C be n × n matrices. Which of the following statements is true?

1. If AB = AC, then it must follow that B = C.
2. If A³ + 2A² + 3A + 5I = 0, then A is nonsingular.
3. If A² = 0, then necessarily A = 0.
4. None of these

Correct answer: If A³ + 2A² + 3A + 5I = 0, then A is nonsingular.

Solution

The statement is true because if A satisfies the polynomial equation A³ + 2A² + 3A + 5I = 0, it implies that the determinant of A cannot be zero, thus A must be nonsingular.

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 →