Q. If $\begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix}\ A\ \begin{bmatrix} - 3 & 2 \\ 5 & - 3 \end{bmatrix} = \ \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ , then $A =$
A) $\begin{bmatrix}
1 & 1 \\
1 & 0
\end{bmatrix}$
B) $\begin{bmatrix}
1 & 1 \\
0 & 1
\end{bmatrix}$
C) $\begin{bmatrix}
1 & 0 \\
1 & 1
\end{bmatrix}$
D) $- \begin{bmatrix}
1 & 1 \\
1 & 0
\end{bmatrix}$
Explanation
(a)
$\begin{bmatrix}
2 & 1 \\
3 & 2
\end{bmatrix}A\begin{bmatrix}
- 3 & 2 \\
5 & - 3
\end{bmatrix} = \ \begin{bmatrix}
1 & 0 \\
0 & 1
\end{bmatrix}$
$A = \begin{bmatrix}
2 & 1 \\
3 & 2
\end{bmatrix}^{- 1}\begin{bmatrix}
1 & 0 \\
0 & 1
\end{bmatrix}\begin{bmatrix}
- 3 & 2 \\
5 & - 3
\end{bmatrix}^{- 1}$
$\Rightarrow A = \begin{bmatrix}
2 & - 1 \\
- 3 & 2
\end{bmatrix}\begin{bmatrix}
1 & 0 \\
0 & 1
\end{bmatrix}\begin{bmatrix}
- 3 & - 2 \\
- 5 & - 3
\end{bmatrix}$
$\Rightarrow A = \begin{bmatrix}
2 & - 1 \\
- 3 & 2
\end{bmatrix}\begin{bmatrix}
3 & 2 \\
5 & 3
\end{bmatrix} = \begin{bmatrix}
1 & 1 \\
1 & 0
\end{bmatrix}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.