# What are Determinants ?

## Minors

Minor of an element aij of a determinant is the determinant obtained by deleting its i th row and j th column in which element aij lies. Minor of an element aij is denoted by Mij.

## Cofactors

Cofactor of an element aij, denoted by Aij is defined by Aij= (-1)i+jMij, where Mij is minor of aij.

## Adjoint And Inverse Of A Square Matrix

The adjoint of a square matrix A = [aij]n×n is defined as the transpose of the matrix [Aij]n×n, where Aij is the cofactor of the element aij. Adjoint of the matrix A is denoted by adj A. If A is a square matrix of order m, and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is called the inverse matrix of A and denoted by A-1.

## Consistency

A system of equations is said to be consistent if its solution (one or more) exists.

## Inconsistency

A system of equations is said to be inconsistent if its solution does not exist.

## Square Matrix

A square matrix A has inverse if and only if A is non- singular ,

## Solution Of Equation

Unique solution of equation AX = B is given by X = A-1B, Where |A| 0