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Question

# Use determinants to decide if the matrix is invertible.$\left[\begin{array}{rr} 2 & -1 \\ -2 & 2 \end{array}\right]$

Solution

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$\textbf{Given:}$ Matrix

$A=\begin{bmatrix} 2 & -1\\ -2 & 2 \end{bmatrix}$

$\textbf{To determine:}$ If $A$ invertible or not by calculating the determinant

$\textbf{Solution:}$ We have

$\text{det} A=\begin{vmatrix} 2 & -1\\ -2 & 2 \end{vmatrix}= 2(2)-(-1)(-2)=4-2=2 \neq 0$

Since the determinant is non zero, thus the given matrix is invertible.

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