If (BA)^{-1} = C where B = begin{bmatrix} 2 & | vedclass

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

Question

(B) Given $(BA)^{-1} = C$. Using the property of inverse matrices $(BA)^{-1} = A^{-1}B^{-1}$,we have $A^{-1}B^{-1} = C$. Multiplying both sides by $B$

Vedclass · Accepted Answer

$\begin{bmatrix} -3 & -5 & -5 \ 0 & 9 & 2 \ 2 & 14 & 6 \end{bmatrix}$

Vedclass · Answer

(B) Given $(BA)^{-1} = C$. Using the property of inverse matrices $(BA)^{-1} = A^{-1}B^{-1}$,we have $A^{-1}B^{-1} = C$. Multiplying both sides by $B$ on the right,we get $A^{-1}B^{-1}B = CB$. Since $B^{-1}B = I$,it follows that $A^{-1} = CB$. Now,calculate the product $CB$: $A^{-1} = \begin{bmatrix} -1 & 0 & 1 \ 1 & 1 & 3 \ 2 & 0 & 2 \end{bmatrix} \begin{bmatrix} 2 & 6 & 4 \ 1 & 0 & 1 \ -1 & 1 & -1 \end{bmatrix}$ $A^{-1} = \begin{bmatrix} (-1)(2) + (0)(1) + (1)(-1) & (-1)(6) + (0)(0) + (1)(1) & (-1)(4) + (0)(1) + (1)(-1) \ (1)(2) + (1)(1) + (3)(-1) & (1)(6) + (1)(0) + (3)(1) & (1)(4) + (1)(1) + (3)(-1) \ (2)(2) + (0)(1) + (2)(-1) & (2)(6) + (0)(0) + (2)(1) & (2)(4) + (0)(1) + (2)(-1) \end{bmatrix}$ $A^{-1} = \begin{bmatrix} -3 & -5 & -5 \ 0 & 9 & 2 \ 2 & 14 & 6 \end{bmatrix}$

If $(BA)^{-1} = C$ where $B = \begin{bmatrix} 2 & 6 & 4 \\ 1 & 0 & 1 \\ -1 & 1 & -1 \end{bmatrix}$ and $C = \begin{bmatrix} -1 & 0 & 1 \\ 1 & 1 & 3 \\ 2 & 0 & 2 \end{bmatrix}$,then $A^{-1}$ is given by

Similar Questions

The element of the second row and third column in the inverse of $\begin{bmatrix} 1 & 2 & 1 \\ 2 & 1 & 0 \\ -1 & 0 & 1 \end{bmatrix}$ is

If $A = \begin{bmatrix} 2 & -1 \\ -1 & 3 \end{bmatrix}$,then the inverse of $(2A^2 + 5A)$ is

Consider the matrices $A = \begin{bmatrix} 2 & -2 \\ 4 & -2 \end{bmatrix}$ and $B = \begin{bmatrix} 3 & 9 \\ 1 & 3 \end{bmatrix}$. If matrices $P$ and $Q$ are such that $PA = B$ and $AQ = B$, then the absolute value of the sum of the diagonal elements of $2(P+Q)$ is . . . . . . .

If matrix $A=\begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix}$ is such that $AX=I$,where $I$ is a $2 \times 2$ unit matrix,then $X=$

If $A = \begin{bmatrix} 2i & i^3 \\ i^2 & 1 \end{bmatrix}$, then $A^{-1}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module