ts together with a binary operation, i.e., an operation combining any two objects to a third, subject to certain requirements.[47] A group in which the objects are matrices and the group operation is matrix multiplication is called a matrix group.[nb 2][48] Since in a group every element has to be invertible, the most general matrix groups are the groups of all invertible matrices of a given size, called the general linear groups.Any property of matrices that is preserved under matrix products and inverses can be used to define further matrix groups. For example, matrices with a given size and with a determinant of 1 form a subgroup of (i.e., a smaller group contained in) their general linear group, called a special linear group.[49] Orthogonal matrices, determined by the conditionMTM = I,form the orthogonal group.[50]  They are called orthogonal since the associated linear transformations of Rn preserve angles in the sense that the scalar product of two vectors is unchanged after 