**Category : **JEE Main & Advanced

In system of linear equations \[AX=B,\,A={{({{a}_{ij}})}_{n\times n}}\] is said to be

(i) Consistent (with unique solution) if \[|A|\ne 0\].

i.e., if \[A\] is non-singular matrix.

(ii) Inconsistent (It has no solution) if \[|A|=0\] and \[(adjA)\,B\] is a non-null matrix.

(iii) Consistent (with infinitely \[m\] any solutions) if \[|A|\,=\,0\] and \[(adj\,A)\,B\] is a null matrix.

*play_arrow*Definition*play_arrow*Order of a Matrix*play_arrow*Equality of Matrices*play_arrow*Types of Matrices*play_arrow*Trace of a Matrix*play_arrow*Addition and Subtraction of Matrices*play_arrow*Scalar Multiplication of Matrices*play_arrow*Multiplication of Matrices*play_arrow*Positive Integral Powers of a Matrix*play_arrow*Transpose of a Matrix*play_arrow*Special Types of Matrices*play_arrow*Adjoint of a Square Matrix*play_arrow*Inverse of a Matrix*play_arrow*Rank of Matrix*play_arrow*Echelon Form of a Matrix*play_arrow*Homogeneous and Non-homogeneous Systems of Linear Equations*play_arrow*Consistency of a System of Linear Equation \[\mathbf{AX=B,}\] where \[\mathbf{A}\] is a square matrix*play_arrow*Cayley-Hamilton Theorem*play_arrow*Geometrical Transformations*play_arrow*Matrices of Rotation of Axes

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