If A= [ ccc 1 & -1 & 0 2 & 3 & 4 0 & 1 & 2 ] and B= [ ccc 2 & 2 &… - Vidyadip

MCQ

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

A
$A^{-1}=B$
B
$A^{-1}=6 B$
C
$B^{-1}=B$
D
$B^{-1}=\frac{1}{6} A$

✓

Answer

We have,
\[\begin{array}{l}
A B=\left[\begin{array}{ccc}
1 & -1 & 0 \\
2 & 3 & 4 \\
0 & 1 & 2
\end{array}\right]\left[\begin{array}{ccc}
2 & 2 & -4 \\
-4 & 2 & -4 \\
2 & -1 & 5
\end{array}\right] \\
=\left[\begin{array}{ccc}
2+4+0 & 2-2+0 & -4+4+0 \\
4-12+8 & 4+6-4 & -8-12+20 \\
0-4+4 & 0+2-2 & 0-4+10
\end{array}\right] \\
=\left[\begin{array}{lll}
6 & 0 & 0 \\
0 & 6 & 0 \\
0 & 0 & 6
\end{array}\right]=61 \Rightarrow B^{-1}=\frac{1}{6} A
\end{array}\]

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