If A and B are square matrices of order 3 suc | vedclass

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

Question

(D) Given that $A$ and $B$ are square matrices of order $n=3$. We are given $|A|=2$ and $|B|=4$. We need to find $|A(\operatorname{adj} B)|$. Using th

Vedclass · Accepted Answer

$32$

Vedclass · Answer

(D) Given that $A$ and $B$ are square matrices of order $n=3$. We are given $|A|=2$ and $|B|=4$. We need to find $|A(\operatorname{adj} B)|$. Using the property of determinants,$|AB| = |A||B|$,we have: $|A(\operatorname{adj} B)| = |A| |\operatorname{adj} B|$. We know that for a square matrix $B$ of order $n$,$|\operatorname{adj} B| = |B|^{n-1}$. Here $n=3$,so $|\operatorname{adj} B| = |B|^{3-1} = |B|^2$. Substituting the values: $|A(\operatorname{adj} B)| = |A| 	imes |B|^2 = 2 	imes (4)^2$. $|A(\operatorname{adj} B)| = 2 	imes 16 = 32$.

If $A$ and $B$ are square matrices of order $3$ such that $|A|=2$ and $|B|=4$,then $|A(\operatorname{adj} B)| = \dots$

Similar Questions

For matrix $A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix}$,$(A^{-1})^2 = $ . . . . . .

If the matrix $A = \begin{bmatrix} 1 & 2 \\ -5 & 1 \end{bmatrix}$ and $A^{-1} = xA + yI$,where $I$ is a unit matrix of order $2$,then the value of $2x + 3y$ is

If $A = \begin{bmatrix} \cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{bmatrix}$ and $A \text{ adj } A = \begin{bmatrix} k & 0 \\ 0 & k \end{bmatrix}$,then $k$ is equal to :-

Find the inverse of the matrix,if it exists: $\left[\begin{array}{cc}3 & 10 \\ 2 & 7\end{array}\right]$

By using elementary operations,find the inverse of the matrix $A=\left[\begin{array}{rr}1 & 2 \\ 2 & -1\end{array}\right]$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module