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Question

If A=2-13-2, then An=

(a) A=1001, if n is an even natural number

(b) A=1001, if n is an odd natural number

(c) A=-1001, if nN

(d) none of these


Solution

Disclaimer: In all option, the power of A (i.e. n is missing)

(a) An=1001, if n is an even natural number

A=2-13-2A2=1001A×A=IA-1=A

Generally,

An=(AA-1)n/2 when n is even.An=A(AA-1)n/2=A when n is odd.Thus, An=I when n is even.

Mathematics
RD Sharma XII Vol 1 (2015)
Standard XII

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