If A is a matrix of order 3,such that A(opera | vedclass

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

Question

(D) We are given the property $A(\operatorname{adj} A) = |A|I$. Comparing this with the given equation $A(\operatorname{adj} A) = 10I$,we get $|A| = 1

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(D) We are given the property $A(\operatorname{adj} A) = |A|I$. Comparing this with the given equation $A(\operatorname{adj} A) = 10I$,we get $|A| = 10$. We know the property for the determinant of the adjoint of a matrix: $|\operatorname{adj} A| = |A|^{n-1}$,where $n$ is the order of the matrix. Here,$n = 3$,so $|\operatorname{adj} A| = |A|^{3-1} = |A|^2$. Substituting the value of $|A|$,we get $|\operatorname{adj} A| = 10^2 = 100$.

If $A$ is a matrix of order $3$,such that $A(\operatorname{adj} A) = 10I$,then $|\operatorname{adj} A| = $

Similar Questions

If $A$ and $B$ are invertible matrices,then which of the following is not correct?

If $A$ is a square matrix such that $A(\operatorname{adj} A) = \begin{bmatrix} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{bmatrix}$, then $\operatorname{det}(\operatorname{adj} A)$ is equal to

If $A$ is a square matrix of order $n$,$|A| = D$,and $|adj(A)| = D'$,then:

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

If the determinant of the adjoint of a (real) matrix of order $3$ is $25$,then the determinant of the inverse of the matrix is

Vedclass Test Series

Exam Paper Generator

Online Exam Module