Q20Comprehension1 Mark7 Aug 2022PassageConsider a matrix A=[abba]A = \begin{bmatrix} a & b \\ b & a \end{bmatrix}A=[abba] and a function f:R2→Rf: \mathbb{R}^2 \to \mathbb{R}f:R2→R such that f(a,b)=det(A)f(a,b) = \det(A)f(a,b)=det(A). Answer the given subquestions:Which of the following options is/are true?AA is not a symmetric matrix for all a, b in R.BA^T is a symmetric matrix for all a, b in R.CIf (β\betaβ, γ\gammaγ) is a critical point of f(a,b), then the matrix A = [βγγβ]\begin{bmatrix} \beta & \gamma \\ \gamma & \beta \end{bmatrix}[βγγβ] satisfies that, A^2 = A.DIf (β\betaβ, γ\gammaγ) is a critical point of f(a,b), then the matrix A = [βγγβ]\begin{bmatrix} \beta & \gamma \\ \gamma & \beta \end{bmatrix}[βγγβ] has rank(A)\text{rank}(A)rank(A) = 1.
