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If A = \(\begin{bmatrix}1 &-1 & 0 \\[0.3em]2 & 3 & 4 \\[0.3em]0 &1 & 2\end{bmatrix}\) and B = \(\begin{bmatrix}2 &2 & -4 \\[0.3em]-4 & 2 & -4 \\[0.3em]2 &-1 & 5\end{bmatrix}\), then :If A = [(1,-1,0)(2,3,4)(0,1,2)] and B = [(2,2,-4)(-4,2,-4)(2,-1,5)], then :(a) A-1 = B(b) A-1 = 6B(c) B-1 = B(d) B-1 = \(\frac{1}{6}\)A |
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Answer» Option : (d) \(AB=\begin{bmatrix}1&-1&0\\2&3&4\\0&1&2\end{bmatrix}\begin{bmatrix}2&2&-4\\-4&2&-4\\2&-1&5\end{bmatrix}=\begin{bmatrix}6&0&0\\0&6&0\\0&0&6\end{bmatrix},\) \(\Rightarrow AB=6I\Rightarrow B^{-1}=\frac{1}{6}A\) |
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