`A = [[p,q],[r,s]]` where p, q, r and s are positive integers. If A is symmetric matrix, `|A|=20` and p = q, then find how many values are possible for s.

The positive integers p ,q ,&r are all primes if p^2-q^2=r , then find all possible values of r

The positive integers p,q,&r are all primes if p^(2)-q^(2)=r, then find all possible values of r

The positive integers p,q and r are all primes if p^(2)-q^(2)=r, then find all possible values of r.

If A = [(p,q),(r,s)] , then express A as the sum of a symmetric and a skew-symmetric matrix.

The positive integers p,q, and r are all primes if p^(2)-q^(2)=r, then find all possible values of r.

If r,s,t are prime numbers and p,q are the positive integers such that LCM of p,q is r^2t^4s^2 , then find the number of ordered pair (p,q).

Let A = [[2,3],[a,0]], a in R be written as P + Q where P is a symmetric matrix and Q is skew symmetric matrix. If det(Q) = 9, then the modulus of the sum of all possible values of determinant of P is equal to :

if p,q,r and s are in proportion then p/q = _________