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Introduction of Determinant

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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)^(th)` element of A. 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 → K is defined by f(A) = k, where A ∈ M and k ∈ K, then f(A) is called the determinant of A. It is also denoted by |A| or det A or ∆.
If A = `[(a,b),(c,d)]` , then determinants of A is written as |A| is written as |A| = `|(a,b),(c,d)|` = det (A)
Remarks: 
(i) For matrix A, |A| is read as determinant of A and not modulus of A. 
(ii) Only square matrices have determinants.

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