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Question

If A=(1012) Find A8=

A
255A254I.
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B
256A255I.
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C
255A255I.
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D
None of these.
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Solution

The correct option is A 255A254I.
A=(1012)
A2=(1012)(1012)=(1034)
Now, 3A2I=(1012)2(1001)

=(3203062)

=(1034)
Hence, A2=3A2I
Now,
A4=(A2)2=(3A2I)2
=9A212AI+4I2
=9A212A+4I
=9(3A2I)12A+4I
=15A14I
A8=(A4)2=(15A14I)2
=225A2420AI+196I2
=225(3A2I)420A+196I
=255A254I

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