If A= [ cc 0 & 1 2 & 3 1 & -1 ] and B= [ lll 1 & 2 & 1 2 & 1 & 0 … - Vidyadip

Question

If $A=\left[\begin{array}{cc}0 & 1 \\ 2 & 3 \\ 1 & -1\end{array}\right]$ and $B=\left[\begin{array}{lll}1 & 2 & 1 \\ 2 & 1 & 0\end{array}\right]$, then find $(A B)^{-1}$

✓

Answer

$A B=\left[\begin{array}{cc}0 & 1 \\ 2 & 3 \\ 1 & -1\end{array}\right]\left[\begin{array}{lll}1 & 2 & 1 \\ 2 & 1 & 0\end{array}\right]$
$=\left[\begin{array}{lll}0+2 & 0+1 & 0+0 \\ 2+6 & 4+3 & 2+0 \\ 1-2 & 2-1 & 1+0\end{array}\right]$
$=\left[\begin{array}{ccc}2 & 1 & 0 \\ 8 & 7 & 2 \\ -1 & 1 & 1\end{array}\right]$
$\therefore|A B|=2\left|\begin{array}{ll}7 & 2 \\ 1 & 1\end{array}\right|-1|8 \quad 2|+0$
$=2(7-2)-(8+2)$
$=10-10$
$=0$
$\therefore(A B)^{-1}$ does not exist.

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