If A=\left[\begin{array}{ccc}a & 0 & 0 \ 0 & a & 0 \ 0 & 0 ...

CBSE Class 12 Math 2020 Outside Delhi Set 3 Solved Paper

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Question : 2 of 11

Marks: +1, -0

If

A={[\table a , 0 , 0 ; 0 , a , 0 ; 0 , 0 , a]}

, then

{\det}({\adj} A)

equals

$a^{27}$
$a^9$
$a^6$
$a^2$

Solution: 👈: Video Solution

a^6

A={[\table a , 0 , 0 ; 0 , a , 0 ; 0 , 0 , a ]}

∴ |A|={[\table a , 0 , 0 ; 0 , a , 0 ; 0 , 0 , a ]}=a^3 ≠ 0

and

n=3

Thus, we have

|{\adj} A|=|A|^{n-1}= (a^3) ^2=a^6

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