Exams › JEE Main › Maths

If the matrix [[α, β], [γ, −α]] is a square root of the 2×2 identity matrix, then which relation must hold?

1. 1 + α² + βγ = 0
2. 1 + α² − βγ = 0
3. 1 − α² + βγ = 0
4. α² + βγ = 1

Correct answer: α² + βγ = 1

Solution

For M=[[a,b],[g,-a]], M^2 = (a^2+bg) I. Setting this equal to the identity requires a^2 + beta*gamma = 1.

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 →