If `A=[[a,0, 0],[ 0,a,0],[ 0, 0,a]]`
, then the value of `|a d j\ A|`
is
`a^(27)`
(b) `a^9`
(c) `a^6`
(d) `a^2`
Text Solution
AI Generated Solution
To find the value of \(|a \cdot \text{adj} A|\) for the matrix \(A = \begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{bmatrix}\), we will follow these steps:
### Step 1: Calculate the Determinant of Matrix A
The determinant of a diagonal matrix is the product of its diagonal elements. Therefore, we have:
\[
|A| = a \cdot a \cdot a = a^3
\]
...
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