If |A| = -3 and A^{-1} = begin{bmatrix} 1 & 0 | vedclass

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

Question

(A) We know that the inverse of a matrix $A$ is given by the formula $A^{-1} = \frac{\operatorname{adj}(A)}{|A|}$.From this,we can express the adjoint

Vedclass · Accepted Answer

$\begin{bmatrix} -3 & 0 & 0 \ 3 & -1 & 0 \ -9 & -2 & 3 \end{bmatrix}$

Vedclass · Answer

(A) We know that the inverse of a matrix $A$ is given by the formula $A^{-1} = \frac{\operatorname{adj}(A)}{|A|}$.From this,we can express the adjoint of $A$ as $\operatorname{adj}(A) = |A| \cdot A^{-1}$.Given $|A| = -3$ and $A^{-1} = \begin{bmatrix} 1 & 0 & 0 \ -1 & \frac{1}{3} & 0 \ 3 & \frac{2}{3} & -1 \end{bmatrix}$.Substituting these values,we get:$\operatorname{adj}(A) = -3 	imes \begin{bmatrix} 1 & 0 & 0 \ -1 & \frac{1}{3} & 0 \ 3 & \frac{2}{3} & -1 \end{bmatrix} = \begin{bmatrix} -3 	imes 1 & -3 	imes 0 & -3 	imes 0 \ -3 	imes (-1) & -3 	imes \frac{1}{3} & -3 	imes 0 \ -3 	imes 3 & -3 	imes \frac{2}{3} & -3 	imes (-1) \end{bmatrix} = \begin{bmatrix} -3 & 0 & 0 \ 3 & -1 & 0 \ -9 & -2 & 3 \end{bmatrix}$.Thus,the correct option is $A$.

If $|A| = -3$ and $A^{-1} = \begin{bmatrix} 1 & 0 & 0 \\ -1 & \frac{1}{3} & 0 \\ 3 & \frac{2}{3} & -1 \end{bmatrix}$,then $(\operatorname{adj} A)$ is

Similar Questions

If $A=\begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}$ and $A^{2}-5A-6I=0$,then $A^{-1}=$

Let $A$ be a $3 \times 3$ matrix such that $|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} A ))|=81$. If $S =\{ n \in \mathbb{Z} :(|\operatorname{adj}(\operatorname{adj} A)|)^{\frac{(n-1)^2}{2}}=|A|^{(3n^2-5n-4)}\}$,then $\sum_{n \in S}|A^{(n^2+n)}|$ is equal to

If $A$ and $B$ are non-singular matrices of the same order,then $\text{Adj}(AB)$ is:

${\left[ {\begin{array}{*{20}{c}}1&3\\3&{10}\end{array}} \right]^{ - 1}} = $

If $A = \begin{bmatrix} 2 & -1 \\ -1 & 2 \end{bmatrix}$ such that $A^2 - 4A + 3I = 0$,where $I$ is a unit matrix of order $2$,then $A^{-1}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module