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A is 3 x 3 metrics and |adj| = 4 then find(i) |2A|(ii) |-3A-1|(iii) A.AdjA |
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Answer» A is matrix of order 3. \(|adjA| = 4\) \(\because |adjA| = |A|^{3 - 1}= |A|^2\) \(\therefore |A|^2 = 4\) ⇒ \(|A| = \pm 2\) (i) \(|2A| = 2^3|A|= 8(\pm2) = \pm 16\) (ii) \(|-3A^{-1}| = (-3)^3 |A^{-1}| = \frac{-27}{|A|} = \frac{-27}{\pm2}= \pm\frac{27}2\) (iii) \(A.adj A = |A|I= \pm 2I= \begin{bmatrix}\pm2&0&0\\0&\pm2&0\\0&0&\pm2\end{bmatrix}\) |
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