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प्रश्न
If A is 3 × 3 invertible matrix, then show that for any scalar k (non-zero), kA is invertible and `("kA")^-1 = 1/"k" "A"^-1`
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उत्तर
We have `("kA") (1/"k" "A"^-1) = ("k". 1/"k") ("A". "A"^-1)` = 1 (I) = 1
Hence (kA) is inverse of `(1/"k" "A"^-1)`
or
`("kA")^-1 = 1/"k" "A"^-1`
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