number of squares on chess board

A matrix in which the number of rows is equal to the number of columns, say n, is called a square matrix of order n. In this square matrix of order n the elements a 1 1 , a 2 2 .......a n n is called the principal diagonal or the leading diagonal. The element..

The adjoint of a square matrix [a i j ] is defined as the transpose of the matrix [A i j ] where A i j are the cofactors of the elements a i j . Adjoint of A is denoted by adj A. ..

A square matrix A is said to be singular if |A| = ..

Matrices : A rectangular array of entries is called a Matrix. The entries may be real, complex or functions. The entries are also called as the elements of the matrix. The rectangular array of entries are enclosed in an ordinary bracket or in square bracket. Determinants : ..

The adjoint of a square matrix [aij] is defined as the transpose of the matrix [Aij] where Aij are the cofactors of the elements aij. Adjoint of A is denoted by adj A. Let A be a square matrix of order n. If there exists a matrix B of order n such that AB = BA = I, ..

Let A = [a ij ] be a square matrix. We can associate with the square matrix A, a determinant which is formed by exactly the same array of elements of the matrix A. A determinant formed by the same array of elements of the square matrix A is called the determinant of th..

Square root of a negative number is known as an imaginary number . If x and y are real numbers, then x + iy is called a complex number . x is called the real part and y is called the imaginary part . The following are the type..

In other words, a square matrix A is invertible if and only if A is a non-singular matrix. (c) If A and B are invertible square matrices, then (AB) - 1 = B - 1 A - 1 (d) If A and B are two non-singular square matrices of the same order, then AB and BA are al..

A rectangular array of entries is called a Matrix. The entries may be real, complex or functions. The entries are also called as the elements of the matrix. The rectangular array of entries are enclosed in an ordinary bracket or in square bracket. Matrices are denoted by capital lette..

Imaginary Number - Square root of a negative number is known as an imaginary number. a > 0 is an imaginary number. or A number whose square is negative is known as an imaginary number. . . . The symbol i, We write, P..