## Singular and Non-singular Matrix

### Definition of Non-singular Matrix

If the determinant of a matrix is not equal to zero, then the matrix is called a non-singular matrix.

### More about Non-singular Matrix

An *n x n*(square) matrix A is called non-singular if there exists an *n x n* matrix *B* such that *AB = BA = I _{n}*, where

*I*, denotes the

_{n}*n x n*identity matrix.

If the matrix is non-singular, then its inverse exists.

Properties of non-singular matrix:

- If
*A*and*B*are non-singular matrices of the same order, then*AB*is non-singular. - If
*A*is non-singular, then*Ak*is non-singular for any positive integer*k*. - If
*A*is non-singular and*k*is a non-zero scalar, then*kA*is non-singular.

### Example of Non-singular Matrix

The determinant of i.e. = 6(3) – 5(2) = 18 - 10 = 8 ≠ 0, so it is a non-singular matrix.

### References & Resources

- N/A

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