We recall that a square matrix is called a non-singular matrix if its determinant is not equal to zero and a square matrix is called singular if its determinant is zero.

**Inverse of a Non-Singular Square Matrix**

We recall that a square matrix is called a **non-singular matrix **if its determinant is
not equal to zero and a square matrix is called **singular **if its determinant is
zero. We have already learnt about multiplication of a matrix by a scalar,
addition of two matrices, and multiplication of two matrices. But a rule could
not be formulated to perform division of a matrix by another matrix since a
matrix is just an arrangement of numbers and has no numerical value. When we
say that, a matrix *A *is of order *n*, we mean that *A *is a
square matrix having *n *rows and *n *columns.

In the case of a real number *x* â‰ 0, there exists a real number y (=1/*x*) called the inverse (or reciprocal) of *x *such that *xy *= *yx *= 1. In the same line of
thinking, when a matrix *A *is given, we search for a matrix *B *such
that the products *AB *and *BA *can be found and *AB *= *BA *= *I *, where *I *is
a unit matrix.

In this section, we define the inverse of a non-singular square
matrix and prove that a non-singular square matrix has a unique inverse. We
will also study some of the properties of inverse matrix. For all these
activities, we need a matrix called the adjoint of a square matrix.

Tags : Applications of Matrices and Determinants , 12th Mathematics : UNIT 1 : Applications of Matrices and Determinants

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12th Mathematics : UNIT 1 : Applications of Matrices and Determinants : Inverse of a Non-Singular Square Matrix | Applications of Matrices and Determinants

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