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Let a and b be two real numbers such that $a > 1, b > 1.$ $I f A = (\begin{matrix} a & 0 \\ 0 & b \end{matrix})$ then $\lim_{n \to \infty} A^{- n}$ is

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Correct option is B

A=a00b⇒A2=a00ba00b =a200b2⇒A3=a200b2a00b =a300b3⇒An=an00bn⇒An−1=1anbnbn00an=a−n00b−n⇒limn→∞ An−1=0000 as a>1 and b>1

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Let a and b be two real numbers such that a> 1, b>1.If A=a00b then limn→∞ A−n is

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Let a and b be two real numbers such that $a > 1, b > 1.$ $I f A = (\begin{matrix} a & 0 \\ 0 & b \end{matrix})$ then $\lim_{n \to \infty} A^{- n}$ is