NIMCET 2012 Question Paper with solutions

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Question : 45 of 120

Marks: +1, -0

If A =

[\table 1,1;0,1]

, then

A^n

for any natural number n is

$[\table n,n;0,n]$
$[\table 1,n;0,1]$
$[\table 1,0;0,1]$
None of these

Solution:

Given,
A =

[\table 1,1;0,1]

Now ,

A^2

= A . A =

[\table 1,1;0,1]

.

[\table 1,1;0,1]

=

[\table 1,2;0,1]

A^2

=

A^2.A

=

[\table 1,2;0,1]

.

[\table 1,1;0,1]

=

[\table 1,3;0,1]

.....
......

A^n

=

[\table 1,n;0,1]

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