Matrix symbol of order two for some banach algebras

Two classes of Banach algebras which admit a matrix symbol of order 2 are described, and an explicit form of the symbol is obtained. Also we describe all polynomials F(X, Y) and F(X, Y, Z) such that the norms of polynomials F(B, B*) ( when B² = 0) and F(S, W, W*) (when S² = I, W² = 0, S* = S) depend only on the polynomial F and on the norms ∥B∥, ∥W∥. Applications to Banach algebras generated by singular integral operators and some their perturbations are considered.