These number systems are accompanied by the arithmetic of addition, subtraction, multiplication, and division. It is about combinatorial estimates associated with arithmetic operations (addition, subtraction, multiplication, and division). His device greatly simplified arithmetic calculations, including multiplication and division. Brahmagupta gave rules for addition, subtraction, multiplication and division. Cayley defined matrix multiplication and matrix inverses. This asymmetry is analogous to the one between integer factorization and integer multiplication. The inverse operation of multiplication is division. Composition of operations corresponds to matrix multiplication. I has instructions for signed and unsigned integer multiplication and division. PM defines analogues of addition, multiplication, and exponentiation for arbitrary relations. The distributive law is valid for matrix multiplication. The greatest lower bound for the exponent of matrix multiplication algorithm is generally called . Further simplification can be obtained by translation of axes and scalar multiplication. The key-feature is the ease of parallel-computation of the Galois field multiplication used for authentication. This can be checked using the distributive property of matrix multiplication.