If `A`
is a square matrix such
that `A(a d j\ A)=[(5, 0, 0),(0, 5, 0),(0, 0, 5)]`
, then write the value
of `|a d j\ A|`
.
Text Solution
AI Generated Solution
To solve the problem, we need to find the value of \(|\text{adj} A|\) given that \(A \cdot \text{adj} A = \begin{pmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{pmatrix}\).
### Step-by-step Solution:
1. **Understanding the Given Information**:
We know that \(A \cdot \text{adj} A = k \cdot I\), where \(k\) is a scalar and \(I\) is the identity matrix. In our case, \(k = 5\), so we can express this as:
\[
A \cdot \text{adj} A = 5I
...
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