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If A is a square matrix of order `2xx2` such that `|A|=27`, then sum of the infinite series `|A|+|1/2A|+|1/4 A|+|1/8 A|+...` is equal to _______ .

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The correct Answer is:
36
`|A|+|1/2A|+|1/4 A|+|1/8 A|+...`
`implies |A|+1/4|A|+1/16|A|+...`
`implies (|A|)/(1-1/4)=4/3|A|=36`
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