Adjoint and Inverse of a Matrix
Adjoint and Inverse of a Matrix: Overview
This topic covers concepts, such as, Singular and Non-singular Matrices, Adjoint of a Matrix, Cofactor Matrix, Properties of Adjoint of Matrices & Inverse of a Matrix Using Adjoint etc.
Important Questions on Adjoint and Inverse of a Matrix
Using matrix method, the solution of the following system of linear equations would be :

Using properties of determinants, the value of
would be:

Let be three matrices such that , and Then the is

Let be a matrix of order and , then the value of is

For any matrix, if , then equals

If is a non-singular matrix, then the value of in terms of is

If the value of a third order determinant is , then the value of the square of the determinant formed by its cofactors will be

If , where represent order matrix. If total number of 's in matrix and matrix are and respectively, then the value of is




If is the adjoint of matrix and then is




If then the order of the square matrix is

Let be a matrix of order such that and , then the value of is

If the value of a third order determinant is , then the value of the determinant formed by replacing each element by its co-factor will be

The adjoint of the matrix is

