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)

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