Business Mathematics and Statistics(EMS) : Matrices and Determinants

**Inverse of a matrix**

A Square matrix A is said to be singular,
if *A*
= 0

A square matrix *A* is said to be non – singular, if
*A* Î 0

The adjoint of a square matrix *A* is defined as the transpose of a
cofactor matrix. Adjoint of the matrix *A*
is denoted by *adj A*

Let *A*
be any non-singular matrix of order *n*.
If there exists a square matrix B of order *n*
such that *AB* = *BA* = *I* then, *B* is called the inverse of A and is
denoted by *A*^{-1}

Consider a system of n linear non – homogeneous
equations with n unknowns *x*_{1}* *,*
x*_{2}, ......*x _{n} *as

**Example 1.22**

The cost of 4 kg onion, 3 kg wheat and 2 kg
rice is `320. The cost of 2kg onion, 4 kg wheat and 6 kg rice is `560. The cost
of 6 kg onion, 2 kg wheat and 3 kg rice is `380. Find the cost of each item per
kg by matrix inversion method.

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11th Business Mathematics and Statistics(EMS) : Chapter 1 : Matrices and Determinants : Inverse of a matrix | Definition, Formula, Solved Example Problems, Exercise | Mathematics

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