**Category : **JEE Main & Advanced

If \[A={{[{{a}_{ij}}]}_{m\times n}}\]and \[B={{[{{b}_{ij}}]}_{m\times n}}\]are two matrices of the same order then their sum \[A+B\] is a matrix whose each element is the sum of corresponding elements i.e., \[A+B={{[{{a}_{ij}}+{{b}_{ij}}]}_{m\times n}}\].

Similarly, their subtraction \[A-B\] is defined as

\[A-B={{[{{a}_{ij}}-{{b}_{ij}}]}_{m\times n}}\]

Matrix addition and subtraction can be possible only when matrices are of the same order.

**Properties of matrix addition** : If A, B and C are matrices of same order, then

(i) \[A+B=B+A\] (Commutative law)

(ii) \[(A+B)+C=A+(B+C)\] (Associative law)

(iii) \[A+O=O+A=A,\]where O is zero matrix which is additive identity of the matrix.

(iv) \[A+(-A)=0=(-A)+A\], where \[(-A)\] is obtained by changing the sign of every element of A, which is additive inverse of the matrix.

(v) \[\left. \begin{align} & A+B=A+C \\ & B+A=C+A \\ \end{align} \right\}\Rightarrow B=C\] (Cancellation law)

*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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