invertible matrix tutorial

Let A be a square matrix of order n. If there exists a matrix B of order n such that AB = BA = I, where I is the identity matrix of order n, then the matrix A is said to be invertible and B is called the inverse (or reciprocal) of ..

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..

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 suc..

Matrix of blood is known as plasma. Nearly 90% of the plasma is represented by water. The organic substances account for about 9% and the remaining 1% is represented by inorganic substances. The organic substances in the plasma occur in a wide variety of forms. There are carbohydrates mos..

A matrix of order m x n whose elements are all 0 is called a null matrix (or zero matrix) of order m x n. It is usually denoted by O or more clearly [O] m , n..

A scalar matrix is a diagonal matrix in which all the diagonal elements are equa..

A matrix having only one row is called a row-matrix. For example: A[1 3 2 -2] is a row matrix of order 1 x..

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

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..

A matrix having only one column is called a column matrix. 3 x 1 and 4 x 1 respectivel..