R= {a0 + a1 i + a2 j + a3 ka0,a1,a2,a3R} is the Quaternion Arena. R R (a0 + a1 i + a2 j + a3 k)= a0 + a2 i + a3 j + a1 k (a 0 + a1 i + a2 j + a3 k) = 0 Obtained R[x;,] a slanted polynomial ring. Suppose : p(x) = 3 + (1 + i + j + k)x + (2 - 2i - 2j - 2k) x^2. q(x) = (1 - i + 2j + 3k) + (2 + i - j + k)x r(x) = (4 + i) + (i - k)x + (2 - i + k) x^2 Test the following equations : (i) p(x)q(x) = q(x)p(x)? (ii) p(x)r(x) = r(x)p(x)? (iii) r(x)q(x) = q(x)r(x)