Properties of Determinants:- Determinant of a matrix is same as the determinant of its transpose. If two rows or columns of a determinant are interchanged the determinant changes its sign. If the elements of a row (column) of a determinant are multiplied by a constant K, then the determinant will be multiplied by the same constant. For example, If A …

Inverse of a Matrix Suppose A is a given matrix. If there exists a matrix B such that, AB = I = BI then A is said to be an invertible matrix and B is called as inverse of A and is denoted by Note:- If a matrix A posses an inverse then A is a square matrix and inverse …

Adjoint of a Matrix If A is a square matrix then the transpose of a matrix obtained by replacing the elements of A by their co-factors is called the adjoint of a matrix A and is denoted by Adj A. For example, Note If A is a square matrix of order ‘3’ and K is any scalar then Adj (KA) …

A is a square matrix. If |A| = 0 , then A is called singular and if |A| ≠ 0 then A is called as a non-singular matrix. Theorems:- If A is a non-singular matrix then If A is non-singular then A has to be invertible. If A, B are non-singular matrices then If A is a non-singular matrix and …

Go here for Matrices EAMCET Part 1 Homogeneous Equations If the system is AX=0 and |A| ≠ 0 then the system has unique solution, that is the zero solution. |A| = 0 then the system has atleast 1 non-zero solution. In-fact the system has infinite number of solutions. If the number of equations in a homogeneous system is less than …