In this paper we consider the algebra M1,1(E) endowed with the involution * induced by the transposition superinvolution of the superalgebra M1,1(F) of 2×2-matrices over the field F. We study the *-polynomial identities for this algebra in the case of characteristic zero. We describe a finite set generating the ideal of its *-identities. We also consider Mn(E), the algebra of n×n matrices over the Grassmann algebra E. We prove that for a large class of involutions defined on it any *-polynomial identity is indeed a polynomial identity. A similar result holds for the verbally prime algebra Mk,l(E). © 2010 Elsevier B.V.2153262275Bahturin, Y., Giambruno, A., Group gradings on associative algebras with involution (2008) Canad. Math. Bull., 51, pp. 182-194Bahturin, Y., Shestakov, I., Zaicev, M., Gradings on simple Jordan and Lie algebras (2005) J. Algebra, 283, pp. 849-868Bahturin, Y., Tvalavadze, M., Tvalavadze, T., Group gradings on superinvolution simple superalgebras (2009) Linear Algebra Appl., 31, pp. 1054-1069Bahturin, Y., Zaicev, M., Involutions on graded matrix algebras (2007) J. Algebra, 315, pp. 527-540Berele, A., Generic verbally prime algebras and their GK-dimensions (1993) Commun. Algebra, 21 (5), pp. 1487-1504Colombo, J., Koshlukov, P., Identities with involution for the matrix algebra of order two over an infinite field of characteristic p (2005) Israel J. Math., 146, pp. 337-356Di Vincenzo, O.M., Koshlukov, P., La Scala, R., Involutions for upper triangular matrix algebra (2006) Adv. Appl. Math., 37, pp. 541-568Drensky, V., Giambruno, A., Cocharacters, codimensions and Hilbert series of the polynomial identities for 2×2 matrices with involution (1994) Canad. J. Math, 46, pp. 718-733Gómez-Ambrosi, C., Shestakov, I.P., On the Lie structure of the skew elements of a simple superalgebra with superinvolution (1998) J. Algebra, 208, pp. 43-71Kac, V.G., Lie superalgebras (1977) Adv. Math., 26, pp. 8-96Kemer, A.R., Varieties and Z2-graded algebras (1985) Math. USSR Izv., 25, pp. 359-374Kemer, A.R., Ideals of identities of associative algebras (1991) AMS Trans. Math. Monogr., 87Knus, M.A., Merkurjev, A., Rost, M., Tignol, J.-P., The book of involutions (1998) Amer. Math. Soc. Colloquium Publ., 44. , AMS, Providence, RILevchenko, D., Finite basis property of identities with involution of a second-order matrix algebra (1982) Serdica, 8 (1), pp. 42-56. , (in Russian)Marcoux, L., Sourour, A., Commutativity preserving linear maps and Lie automorphisms of triangular matrix algebras (1999) Linear Algebra Appl., 288, pp. 89-104Racine, M.L., Primitive superalgebras with superinvolution (1998) J. Algebra, 206, pp. 588-614Rowen, L.H., (1980) Polynomial Identities in Ring Theory, , Academic Press, New York