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Question

Let a and b be two real numbers such that a>1,b>1. If A=(a00b), then limn(A1)n is

A
unit matrix
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B
null matrix
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C
2I, where I is the identity matrix.
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D
None of these
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Solution

The correct option is B null matrix
A=(a00b)
A2=(a00b)(a00b)=(a200b2)
A3=(a200b2)(a00b)=(a300b3)

An=(an00bn)
(An)1=1anbn(bn00an)=(an00bn)

As a>1,b>1, an and bn both tends to zero as n
limn(An)1=limn(A1)n=(0000)

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