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:
\[
\text{LHS} = |A \cdot \text{adj} A|
\]
...
Topper's Solved these Questions
ADJOINTS AND INVERSE OF MATRIX
RD SHARMA|Exercise QUESTION|1 Videos
ALGEBRA OF MATRICES
RD SHARMA|Exercise Solved Examples And Exercises|410 Videos
Similar Questions
Explore conceptually related problems
If A is a square matrix of order n, prove that |AadjA|=|A|^(n).
If A is a square matrix of order n then |kA|=
If A is a square matrix of order n such that |adj(adjA)|=|A|^(9), then the value of n can be 4 b.2 c.either 4 or 2 d.none of these
If A is a singular matrix of order n, then (adjA) is
If A is a singular matrix of order n, then A(adjA)=
If A and B are square matrices of order n , then prove that Aa n dB will commute iff A-lambdaIa n dB-lambdaI commute for every scalar lambdadot
If A is a square matrix of order n and |A|=D, |adjA|=D' , then
If A is a square matrix of order n, where |A|=5 and |A(adjA)|= 125 , then n=
If A is a square matrix of order n and AA^(T)=I then find |A|
