If A is a square matrix of order 3,then |oper | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) We know that for a square matrix $M$ of order $n$,$|\operatorname{adj} M| = |M|^{n-1}$.Given $A$ is a square matrix of order $n=3$.First,consider

Vedclass · Accepted Answer

$|A|^8$

Vedclass · Answer

(C) We know that for a square matrix $M$ of order $n$,$|\operatorname{adj} M| = |M|^{n-1}$.Given $A$ is a square matrix of order $n=3$.First,consider the matrix $M = A^2$. The order of $M$ is $3$.Then,$|\operatorname{adj} M| = |M|^{3-1} = |M|^2 = (|A|^2)^2 = |A|^4$.Now,we need to find $|\operatorname{adj}(\operatorname{adj} A^2)|$.Let $K = \operatorname{adj} A^2$. Then $|K| = |A|^4$.Using the property $|\operatorname{adj} K| = |K|^{n-1}$,where $n=3$:$|\operatorname{adj} K| = |K|^{3-1} = |K|^2$.Substituting $|K| = |A|^4$:$|\operatorname{adj}(\operatorname{adj} A^2)| = (|A|^4)^2 = |A|^8$.

If $A$ is a square matrix of order $3$,then $|\operatorname{Adj}(\operatorname{Adj} A^2)|=$

Similar Questions

Find the inverse of the matrix (if it exists): $\left[\begin{array}{lll}1 & 2 & 3 \\ 0 & 2 & 4 \\ 0 & 0 & 5\end{array}\right]$

If $P$ is a $3 \times 3$ real matrix such that $P^{T} = aP + (a - 1)I$,where $a > 1$,then $..........$

Let $A = \begin{bmatrix} 1 & 2 \\ -1 & 4 \end{bmatrix}$. If $A^{-1} = \alpha I + \beta A$,where $\alpha, \beta \in \mathbb{R}$ and $I$ is a $2 \times 2$ identity matrix,then $4(\alpha - \beta)$ is equal to:

If $A = \begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix}$,then $A(\text{adj } A) = $

If $A = \begin{bmatrix} 3 & 4 \\ 5 & 7 \end{bmatrix}$,then $A(adj A) = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module