If A= 1&2&x 0&1&0 0&0&1 and B= 1&-2&y 0&1&0 0&0&1 and A B=I_3, th… - Vidyadip

MCQ

If $\text{A}=\begin{bmatrix}1&2&\text{x}\\0&1&0\\0&0&1\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&-2&\text{y}\\0&1&0\\0&0&1\end{bmatrix}$ and $A B=I_3$, then $x+y$ equals :

✓
$0$
B
$-1$
C
$2$
D
None of these.

✓

Answer

Correct option: A.

$0$

Given : $A B=I_3$
$\Rightarrow\begin{bmatrix}1&2&\text{x}\\0&1&0\\0&0&1\end{bmatrix}\begin{bmatrix}1&-2&\text{y}\\0&1&0\\0&0&1\end{bmatrix}=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$
$\Rightarrow\begin{bmatrix}1&0&\text{y+x}\\0&1&0\\0&0&1\end{bmatrix}=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$
The corresponding elements of two equal matrices are equal.
$\therefore\ \text{y}+\text{x}=0$

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