There are many applications of matrices and determinants. One of the application is to find area of triangle if we are given with vertices of triangle.
Properties of Adjoint of Matrices
This post is dedicated to some important properties regarding adjoint of matrix. If, you want to go through their proves then click particular property. Note that these properties are only valid for square matrices as adjoint is only valid for square matrices.
where, A is a square matrix, I is an identity matrix of same order as of A and
represents determinant of matrix A.
determinant of adjoint A is equal to determinant of A power n-1 where A is invertible n x n square matrix.
{A is n x n invertible square matrix}
You can also take examples to verify these properties.
Inverse of any Matrix is unique
In this post, I am going to discuss few properties regarding inverse of matrices and its uniqueness. If, we have any square matrix A then we cannot have more than one inverse of matrix A. In other words, we can say that inverse of any matrix is unique.
How to find Inverse of a Matrix ?
Inverse of matrix is calculated using adjoint and determinant of matrix. The inverse of matrix A = adj (A) /|A| i.e inverse of any matrix A is equal to adjoint of A divided by determinant of A. In the last posts, I discussed about calculating adjoint and determinant of matrices.
How to find Adjoint of Matrix ?
In the last posts, I discussed about finding co-factors of all the elements present in the matrix. To find adjoint of a given matrix, we simply replace all the elements present in the matrix by their co-factors and then we take transpose of the matrix. The resultant matrix is the
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