Check sibling questions

Suppose we have

  (−1) 2 = −1 × −1

 = 1

 

  (−1) 3 = −1 × −1 × −1

 = 1 × −1

 = −1

 

  (−1) 4 = −1 × −1 × −1 × −1

 = 1 × 1

 = 1

 

  (−1) 5 = −1 × −1 × −1 × −1 × −1

 = 1 × 1 × −1

 = −1

 

  (−1) 6 = −1 × −1 × −1 × −1 × −1 × −1

 = 1 × 1 × 1

 = 1

 

  (−1) 7 = −1 × −1 × −1 × −1 × −1 × −1 × −1

 = 1 × 1 × 1 × −1

 = −1

 

  (−1) 8 = −1 × −1 × −1 × −1 × −1 × −1 × −1 × −1

= 1 × 1 × 1 × 1

= 1

 

  (−1) 9 = −1 × −1 × −1 × −1 × −1 × −1 × −1 × −1 × −1

 = 1 × 1 × 1 × 1 × −1

 = −1

 

  (−1) 10 = −1 × −1 × −1 × −1 × −1 × −1 × −1 × −1 × −1 × −1

 = 1 × 1 × 1 × 1 × 1 × 1

 = 1

 

So, we see that

  (−1) odd number = −1

  (−1) even number = 1

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.