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Question

Suppose A is any 3×3 non-singular matrix and (A3I)(A5I)=O, where I=I3 and O=O3. If αA+βA1=4I, then α+β is equal to :

A
13
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B
7
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C
12
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D
8
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Solution

The correct option is D 8
(A3I)(A5I)=O
A28AI+15=0
A8I+15A1=0
A+15A1=8I
12A+152A1=4I
α=12 and β=152
Hence, α+β=8

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