Question

Give Some Information on : Determinant

Answer 1

@abhi_abhi

Answer 2

For any square matrix of order 2, we have found a necessary and sufficient condition for invertibility. Indeed, consider the matrix



The matrix A is invertible if and only if . We called this number the determinant of A. It is clear from this, that we would like to have a similar result for bigger matrices (meaning higher orders). So is there a similar notion of determinant for any square matrix, which determines whether a square matrix is invertible or not?
In order to generalize such notion to higher orders, we will need to study the determinant and see what kind of properties it satisfies. First let us use the following notation for the determinant