If A and B are non-singular matrices and oper | vedclass

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

Question

(C) We know that for any non-singular matrix $M$,$M^{-1} = \frac{\operatorname{Adj}(M)}{\operatorname{det}(M)}$,which implies $\operatorname{Adj}(M) =

Vedclass · Accepted Answer

$\operatorname{Adj}(AB)$

Vedclass · Answer

(C) We know that for any non-singular matrix $M$,$M^{-1} = \frac{\operatorname{Adj}(M)}{\operatorname{det}(M)}$,which implies $\operatorname{Adj}(M) = \operatorname{det}(M) \cdot M^{-1}$.Given the expression $((\operatorname{det} A)(\operatorname{det} B)) B^{-1} A^{-1}$.Since $\operatorname{det}(AB) = \operatorname{det}(A) \cdot \operatorname{det}(B)$,we can write the expression as $\operatorname{det}(AB) \cdot (B^{-1} A^{-1})$.Using the property of matrix inversion,$(AB)^{-1} = B^{-1} A^{-1}$.Therefore,the expression becomes $\operatorname{det}(AB) \cdot (AB)^{-1}$.By the definition of the adjoint matrix,this is equal to $\operatorname{Adj}(AB)$.

If $A$ and $B$ are non-singular matrices and $\operatorname{det}(AB)=(\operatorname{det} A)(\operatorname{det} B)$,then $((\operatorname{det} A)(\operatorname{det} B)) B^{-1} A^{-1} =$

Similar Questions

If $A=\left[\begin{array}{ccc}1 & 2 & 1 \\ -1 & 1 & 3\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & 2 \\ -3 & 1 \\ 0 & 2\end{array}\right]$,then find $(AB)^{-1}$.

If $A=\left[\begin{array}{ccc}1 & -2 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4\end{array}\right]$,then $A \cdot \operatorname{adj}(A)$ is equal to

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 :-

If $A = f(x) = \begin{bmatrix} \cos x & \sin x & 0 \\ -\sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix}$,then $A^{-1}$ is equal to:

Find the inverse of the matrix $A = \left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$,if it exists.

Vedclass Test Series

Exam Paper Generator

Online Exam Module