If [ * 20 c 2&1 1&2 ] A [ * 20 c - 3 &2 5& - 3 ] = I_2 then A = - Vidyadip

MCQ

If $\left[ {\begin{array}{*{20}{c}}
2&1 \\
1&2
\end{array}} \right]$ $A\left[ {\begin{array}{*{20}{c}}
{ - 3}&2 \\
5&{ - 3}
\end{array}} \right] = {I_2}$ then $A =$

✓
$\left[ {\begin{array}{*{20}{c}}
1&1 \\
1&0
\end{array}} \right]$
B
$\left[ {\begin{array}{*{20}{c}}
1&1 \\
0&1
\end{array}} \right]$
C
$\left[ {\begin{array}{*{20}{c}}
1&0 \\
1&1
\end{array}} \right]$
D
$\left[ {\begin{array}{*{20}{c}}
0&1 \\
1&1
\end{array}} \right]$

✓

Answer

Correct option: A.

$\left[ {\begin{array}{*{20}{c}}
1&1 \\
1&0
\end{array}} \right]$

a
$\left[\begin{array}{ll}{2} & {1} \\ {3} & {2}\end{array}\right] {A}\left[\begin{array}{cc}{-3} & {2} \\ {5} & {-3}\end{array}\right]=\left[\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\right]$

$\left[\begin{array}{ll}{2} & {1} \\ {3} & {2}\end{array}\right] \mathrm{A}=\left[\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\right]\left[\begin{array}{ll}{-3} & {2} \\ {5} & {-3}\end{array}\right]^{-1}$

$A=\left[\begin{array}{ll}{2} & {1} \\ {3} & {2}\end{array}\right]^{-1}\left[\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\right]\left[\begin{array}{cc}{-3} & {2} \\ {5} & {-3}\end{array}\right]^{-1}$

$=\frac{1}{1}\left[\begin{array}{cc}{2} & {1} \\ {3} & {2}\end{array}\right] \frac{1}{-1}\left[\begin{array}{cc}{-3} & {-2} \\ {-5} & {-3}\end{array}\right]$

$=\left[\begin{array}{cc}{2} & {-1} \\ {-2} & {2}\end{array}\right]\left[\begin{array}{cc}{3} & {2} \\ {5} & {3}\end{array}\right]$

$ \Rightarrow\left[\begin{array}{cc}{6-5} & {4-3} \\ {-9+10} & {-6+6}\end{array}\right]=\left[\begin{array}{cc}{1} & {1} \\ {1} & {0}\end{array}\right]$

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