Q1-Let-M-2-be-the-set-of-square-matrices-of-order-2-over-the-real-number-system-and-R-A-B-M-2-M-2-A-P-T-BP-for-some-non-singular-P-M-Then-R-is-A-symmetric-B-transit

Question Number 119797 by Ar Brandon last updated on 27/Oct/20

Q 1

Let M_{2} be the set of square matrices of order 2 over

the real number system and

R = {(A, B) \in M_{2} \times M_{2} ∣ A = P^{T} B P for some

non - singular P \in M}

Then R is

(A) symmetric

(B) transitive

(C) reflexive on M_{2}

(D) not an equivalence relation on M_{2}

Q 2

For any integer n, let I_{n} be the interval (n, n + 1) .

Define

R = {(x, y) \in R ∣ both x, y \in I_{n} for some n \in Z}

Then R is

(A) reflexive on R

(B) symmetric

(C) transitive

(D) an equivalence relation