MCQ
If $A=\left[\begin{array}{rr}2 & 1 \\ -1 & 2\end{array}\right], B=\left[\begin{array}{rr}1 & -2 \\ 2 & 1\end{array}\right], C=\left[\begin{array}{rr}1 & -3 \\ 2 & 1\end{array}\right]$,then
  • $\text{A+B=B+A}$ and $\text{A+(B+C)=(A+B)+C}$
  • B
    $\text{A+B=B+A}$ and $\text{AC=BC}$
  • C
    $\text{A+B=B+A}$ and $\text{AB=BC}$
  • D
    $\text{AC=BC}$ and $\text{A=BC}$

Answer

Correct option: A.
$\text{A+B=B+A}$ and $\text{A+(B+C)=(A+B)+C}$
In option $(a),$ there are two laws, commutative law and associative law, which are satisfied by all matrices. Thus, option $(a)$ is correct.

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