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KCET2013MathematicsDeterminants

If A= [ array cc & 2 2 & array ] and |A³ |=125 , then is equal to

Options

  1. A1
  2. B2
  3. C3
  4. D5

Correct answer

C. 3

Step-by-step solution

Given, A= [ array ll & 2 2 & array ] Now, |A|= | array cc & 2 2 & array |= ²-4...(i) Also, given, array ll & |A³ |=125 & |A|³=125=(5)³ ( |A^ n |=|A|^ n ) & |A|=5 array On putting this value in Eq. (i), we get aligned 5 &= ²-4 ² &=9=(3)² &= 3 aligned

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