number properties and number operations

The Algebraic Properties of set operations are: Idempotent laws, Identity laws, Commutative laws, Associative laws, Distributive laws, De Morgan's Law..

Equality of Matrices, Addition of Matrices, Matrix Addition is commutative, Matrix addition is associative, Subtraction of Matrices, Multiplication of a matrix by a scalar, Multiplication of Matrices, Properties of Matrix Multiplication, Transpose of a Matrix, Properties o..

Summary - A well-defined collection of definite objects is called a set. In roster method of representing a set, all the elements are listed in the set. In property method of representing a set, all the elements are represented by stating all the properties which are satisfied b..

Equality of Matrices - Two matrices are said to be equal if they have the same order and their corresponding elements are equal. e.g., then a = 1, b = 2, c = 3, d = 4, e = 5 and f = ..

The Properties of proportions are: Invertendo, Alternendo, Componendo, Dividendo, Componendo and Dividend..

If the rows and columns of a determinant are inter-changed, the value remains unaltered. If any two rows (columns) of a determinant are identical, its value of the determinant is zero. If any two rows (columns) of a determinant are interchanged, the value of the determinant is (-1) times th..

Invertendo - If a:b=c:d then b:a = d:c a:b=c:d Dividing 1 by each of these ratio..

Properties of Complex numbers - If Z, Z 1 and Z 2 are complex numbers, th..

The Properties of Matrices are: Commutative property, Distributive property, Associative property, additive inverse property. Zero matrix possesses identity property of additio..

(1) A x I = I x A = A where I denotes a unit matrix of suitable order. Matrix I possesses identity property of multiplication, I is called a unit matrix or identity matrix. (2) , it does not have commutative property. (3) A(B + C) = AB + AC (Distributive property) ..