# Matrix Chapter-9

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Determinant of a Matrix: A determinant is a unique number associated with a square matrix. A Determinant can be denoted either as |A| or as det(A).

The determinant tells us things about the matrix that is useful in systems of linear equations, helps us find the inverse of a matrix, useful in calculus and more. The determinant det(A) of a matrix A is non-zero if and only if A is invertible or, yet another equivalent statement, if its rank equals the size of the matrix.

How to Compute the Determinant of 2*2 matrix: Suppose A is a below given matrix then determinant of the matrix is calculated as per equation given.

|A| = (A11 * A22) – (A12 * A21)

How to Compute the Determinant of 3*3 Matrix: Suppose A is a below given matrix then determinant of the matrix is calculated as per equation given.

|A| = A11 (A22*A33 – A32*A23) – A12 (A21*A33 – A31*A23) + A13 (A21*A32 – A22*A31)