Difference between matrix and determinant

1. A matrix 'A' cannot be reduced to a number whereas the determinant can be reduced to a number. 
2. The number of rows may not be equal to number of columns in a matrix while in a determinant the number of rows is equal to the number of columns 
3. Interchanging the rows and columns, a different matrix is formed while a determinant, an interchange of rows and columns doesn't change the value of the determinant. 

Note : Every square matrix(same order like -1x1, 2x2,... nxn)  have determinant
But those, which are not square matrix( like 1x2,2x3,3x4...)they dose not possess determinant.

We have a matrix A. 

Then the determinant of a matrix A can be written as -
|A| and detA

 

By solving above determinant, we get