A triangular matrix is a special form of square matrix and can be either an upper triangular matrix or a lower triangular matrix. An upper triangular matrix occurs where all the entries below the main diagonal are zero, and a lower triangular matrix is where all the entries above the main diagonal are zero. Triangular matrices are the easiest way to find the determinant of a matrix.
The determinant of a matrix is a specific number that can be calculated from any given square matrix. A square matrix, as the name suggests, has the same number of rows as columns. When calculating the determinant of a matrix, converting the matrix into a triangular matrix is the simplest way. This can be achieved by performing a series of row operations that transform the square matrix into a triangular matrix, and then the determinant of the matrix can be readily found from the product of the diagonal entries of the triangular matrix. The determinant of a matrix is an extremely important value that provides useful information about the matrix, and it can be used to solve a system of linear equations, find the inverse of the given matrix and solve problems in calculus, among other uses.