If A = {bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 ... - CBSE Class 12 ...

CBSE Class 12 Math 2020 Outside Delhi Set 3 Solved Paper

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Question : 2 of 11

Marks: +1, -0

If

A = \begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{bmatrix}

, then

\det(\operatorname{adj} A)

equals

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

Solution: 👈: Video Solution

a^6

A = \begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{bmatrix}

\therefore |A| = \begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{bmatrix} = a^3 \neq 0

and

n=3

Thus, we have

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

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