If `A`
is a square matrix of order `n ,`
prove that `|Aa d jA|=|A|^n`
Text Solution
AI Generated Solution
To prove that \( |A \cdot \text{adj} A| = |A|^n \) for a square matrix \( A \) of order \( n \), we can follow these steps:
### Step 1: Write down the left-hand side (LHS)
We start with the left-hand side of the equation we want to prove:
\[
\text{LHS} = |A \cdot \text{adj} A|
\]
...
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Knowledge Check
If A is a square matrix of order n then |kA|=
A
`K|A|`
B
`k^(n)|A|`
C
`k^(-n)|A|`
D
`|A|`
If A is a singular matrix of order n, then (adjA) is
A
symmetric
B
singular
C
non-singular
D
not defined
If A is a singular matrix of order n, then A(adjA)=
A
`0`
B
`A`
C
`I`
D
`|A|I_n`
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