If A = begin{bmatrix} 2 & -1 3 & -2 end{bmat | vedclass

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

Question

(A) Given $A = \begin{bmatrix} 2 & -1 \ 3 & -2 \end{bmatrix}$.First,we calculate the determinant of $A$:$|A| = (2)(-2) - (-1)(3) = -4 + 3 = -1$.Since

Vedclass · Accepted Answer

$A$

Vedclass · Answer

(A) Given $A = \begin{bmatrix} 2 & -1 \ 3 & -2 \end{bmatrix}$.First,we calculate the determinant of $A$:$|A| = (2)(-2) - (-1)(3) = -4 + 3 = -1$.Since $|A| 
eq 0$,$A$ is invertible.Now,calculate $A^2$:$A^2 = \begin{bmatrix} 2 & -1 \ 3 & -2 \end{bmatrix} \begin{bmatrix} 2 & -1 \ 3 & -2 \end{bmatrix} = \begin{bmatrix} 4-3 & -2+2 \ 6-6 & -3+4 \end{bmatrix} = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix} = I$.Since $A^2 = I$,we can find $A^3$:$A^3 = A^2 \cdot A = I \cdot A = A$.We need to find the inverse of $A^3$,which is $(A^3)^{-1}$.Since $A^3 = A$,then $(A^3)^{-1} = A^{-1}$.From $A^2 = I$,we know that $A \cdot A = I$,which implies $A^{-1} = A$.Therefore,$(A^3)^{-1} = A$.

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

Similar Questions

If $A = \begin{bmatrix} 1 & a & 3 \\ 1 & 1 & 5 \\ 2 & 4 & 7 \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} 13 & 2 & -7 \\ -3 & b & 2 \\ -2 & 0 & 1 \end{bmatrix}$,then the values of $a$ and $b$ are respectively

If $A$ is a non-singular matrix and $A^2 - A + I = 0$, then $A^{-1} = \dots$

If $B$ is the inverse of a third order matrix $A$ and $\det B = k$,then $(\operatorname{adj}(\operatorname{adj} A))^{-1} =$

Let $A = \begin{bmatrix} 1 & 0 & 0 \\ 5 & 2 & 0 \\ -1 & 6 & 1 \end{bmatrix}$,then the adjoint of $A$ is

If $Q$ is the inverse of $A$,where $A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{bmatrix}$ and $10Q = \begin{bmatrix} 4 & 2 & 2 \\ -5 & 0 & x \\ 1 & -2 & 3 \end{bmatrix}$,find $x$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module