Question

If $A=\left[\begin{array}{cc}2& 1\\ -1& 3\end{array}\right],B=\left[\begin{array}{cc}-3& 2\\ 4& 1\end{array}\right],C=\left[\begin{array}{cc}-3& 2\\ 4& 1\end{array}\right]$, verify the following :

(i) $A+B=B+A$

Answer 1

Step1: Calculation of the matrix $A+B$.

The addition of matrices having the same order is defined as the addition of corresponding elements of two or more matrices.

$\begin{array}{rcl}A+B& =& \left[\begin{array}{cc}2& 1\\ -1& 3\end{array}\right]+\left[\begin{array}{cc}-3& 2\\ 4& 1\end{array}\right]\\ & =& \left[\begin{array}{cc}2-3& 1+2\\ -1+4& 3+1\end{array}\right]\\ & =& \left[\begin{array}{cc}-1& 3\\ 3& 4\end{array}\right]\end{array}$

Step2: Calculation of the matrix $B+A$.

$\begin{array}{rcl}B+A& =& \left[\begin{array}{cc}-3& 2\\ 4& 1\end{array}\right]+\left[\begin{array}{cc}2& 1\\ -1& 3\end{array}\right]\\ & =& \left[\begin{array}{cc}-3+2& 2+1\\ 4-1& 1+3\end{array}\right]\\ & =& \left[\begin{array}{cc}-1& 3\\ 3& 4\end{array}\right]\end{array}$

Conclusion: The relation is verified.