If `alpha,beta,gamma` are three real numbers and `A=[(1,"cos"(alpha-beta),"cos"(alpha-gamma)),(cos(beta-alpha),1,"cos"(beta-gamma)),("cos"(gamma-alpha),"cos"(gamma-beta),1)]` , then which of following is/are true? a.`A` is singular b. `A` is symmetric c. `A` is orthogonal d. `A` is not invertible

Options

A. A is singular
B. A is symmetric
C. A is orthogonal
D. A is not invertible

Answer

A, B, D

Explanation

`A=[(cos alpha,sin alpha,0),(cos beta,sin beta,0),(cos gamma,sin gamma,0)][(cos alpha,cos beta,cos gamma),(sin alpha,sin beta,sin gamma),(0,0,0)]`
Clearly, A is symmetric and `|A|=0`, hence, singular and not invertiable. Also,
`A A^(T) ne 1`