Properties of Matrix Addition

Q.

Which is the following is true about addition of matrices.

1. Addition of matrices can be performed only on two matrices of the same orders.

2. Addition of matrices can be performed on two matrices which are not necessarily of same order.

3. The resultant matrix obtained after addition of two matrices is of the same order as the order of two original matrices.

4. None of these

Q.

How do you add $2\times 2$ matrices?

Q. If the sum of three matrices is given as
$A+(B+C)=\left[\begin{array}{ccc}0& 5& 4\\ 5& 8& 2\\ 6& 0& 0\end{array}\right],$
then what is $(A+B)+C?$

1. $\left[\begin{array}{ccc}0& 5& 4\\ 5& 8& 2\\ 6& 0& 0\end{array}\right]$
2. $\left[\begin{array}{ccc}0& 5& 6\\ 5& 8& 0\\ 4& 2& 0\end{array}\right]$
3. $\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]$
4. Cannot determine

Q.

If A = $\left[\begin{array}{cc}0& 2\\ 3& 5\end{array}\right]$, B = $\left[\begin{array}{ccc}3& 4& 5\\ 2& 3& 1\\ 1& 3& 7\end{array}\right]$, then A + B =

1. $\left[\begin{array}{cc}3& 6\\ 5& 8\end{array}\right]$

2. $\left[\begin{array}{cc}3& 5\\ 6& 8\end{array}\right]$

3. $\left[\begin{array}{cc}0& 1\\ 3& 5\end{array}\right]$

4. None of these

Q. Which of the following is/are true for matrix addition and scalar multiplication?

1. $A+B=B+A$
2. $\left(pq\right)A=p\left(qA\right)$
3. $p(A+B)=pA+B$
4. $IA=A$