Math  /  Algebra

QuestionUse the fact that if A=[abcd]A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right], then A1=1adbc[dbca]A^{-1}=\frac{1}{a d-b c}\left[\begin{array}{rr}d & -b \\ -c & a\end{array}\right] to find the inverse of the given matrix, if possible. Check that AA1=I2A A^{-1}=I_{2} and A1A=I2A^{-1} A=I_{2}. A=[2211]A=\left[\begin{array}{rr} 2 & -2 \\ -1 & 1 \end{array}\right]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. A1=A^{-1}= \square (Simplify your answer.) B. The inverse matrix is not possible.

Studdy Solution
Since the determinant is zero, the inverse of matrix A A does not exist. Therefore, the correct choice is:
B. The inverse matrix is not possible.

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