Determinants

To every square matrix \(A=[a_{ij}]\) of order n, we can associate a number (real or complex) called determinant of the square matrix A, where \(a_{ij}=(i,j)^{ih}\) element of A. Reprint 2025-26 This may be thought of as a function which associates each square matrix with a unique number (real or complex). If M is the set of square matrices, K is the set of numbers (real or complex) and \(f:M\rightarrow K\) is defined by \(f(A)=k\) where \(A\in M\) and \(k\in K\), then \(f(A)\) is called the determinant of A. It is also denoted by | \(|A|\) or det A or A.

If \(A=[\begin{smallmatrix}a&b\\ c&d\end{smallmatrix}],\) then determinant of A is written as \(|A|=|\begin{smallmatrix}a&b\\ c&d\end{smallmatrix}|=det(A)\)