In getting the inverse matrix of square matrix traditionally, people use the Gauss-Jordan Elimination. With these, the researchers thought of deriving a method to obtain the inverse matrix of square matrices. To get the inverse matrix of square matrices, the researchers used the matrix of the determinants by multiplying the reciprocal of the determinant time the cofactors of the matrix. The following are the steps in doing this:
First step solve for the reciprocal of the determinant of a given square matrix (Note if the determinant of the matrix is 0 then there is no inverse matrix).
Second step is to solve the cofactors.
Third step is to get the transpose of the cofactors (note it is the changing of the column to row and row to column).
Fourth step is to get the product of the result of the first step and the result of the second step.
And the fifth step is to check if the result of the fourth step is the inverse of the given matrix by multiplying the given matrix to the inverse matrix. If the resulting product is the identity matrix then the inverse is correct. (M-1M=I, MM-1=I).
The following terms and concepts are useful in understanding this paper.
MATRIX is a rectangular table of elements (or entries), which may be numbers or, more generally, any abstract quantities that can be added and multiplied. Matrices are used to describe linear equations, keep track of the coefficients of linear transformations and to record data that depend on multiple parameters. Matrices as described by the field of matrix theory can be added, multiplied, and decomposed in various ways, which also makes them a key concept in the field of linear algebra.
TRANSPOSE of a matrix is the matrix formed by turning the rows into columns and the columns into rows.
SQUARE MATRIX is a matrix which has the same number of rows and columns.
IDENTITY MATRIX -of size n is the n-by-n matrix in which all the elements on the main diagonal are equal to 1 and all other...