A determinant is a special number that can be computed from a square matrix that tells us some of the properties and uses of the matrix. There are many ways to find determinants, including diagonal, algebraic congruent, equivalence, and inverse ordinal numbers. These methods are described below:
Diagonal method: The matrix is transformed into an upper or lower triangle matrix, and then the determinant value is calculated by multiplying and adding the diagonal elements.
Algebraic coundit method: Multiply the algebraic coundant by (-1) to the power and add it up.
Equivalence transformation method: The matrix is transformed into a simpler form, such as a stepped matrix or a diagonal matrix, through a series of row transformations, and then the determinant is found according to the matrix of the simple form.
Inverse ordinal method: Uses the concept of inverse ordinal numbers in permutations and combinations to solve the determinant by calculating the sum of the inverse ordinal numbers of all elements.
In addition, the determinant of the matrix can be found by using the multiplicative and additive properties of the determinant. When dealing with larger matrices, we can use a matrix calculator to simplify the calculation process. At the same time, for the determinant after adding a row of columns, we can choose different strategies according to the number of rows and columns that increase or decrease, such as expanding by multiple rows and columns or applying the addition method to add vacant rows (columns), etc.