If A = begin{bmatrix} 0 & 1 & 2 1 & 2 & 3 3 | vedclass

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(D) We know that $AA^{-1} = I$. Multiplying the given matrices: $\begin{bmatrix} 0 & 1 & 2 \ 1 & 2 & 3 \ 3 & a & 1 \end{bmatrix} 	imes \frac{1}{2}

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$1, -1$

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(D) We know that $AA^{-1} = I$. Multiplying the given matrices: $\begin{bmatrix} 0 & 1 & 2 \ 1 & 2 & 3 \ 3 & a & 1 \end{bmatrix} 	imes \frac{1}{2} \begin{bmatrix} 1 & -1 & 1 \ -8 & 6 & 2c \ 5 & -3 & 1 \end{bmatrix} = I$ $\frac{1}{2} \begin{bmatrix} 0 & 1 & 2 \ 1 & 2 & 3 \ 3 & a & 1 \end{bmatrix} \begin{bmatrix} 1 & -1 & 1 \ -8 & 6 & 2c \ 5 & -3 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix}$ Performing matrix multiplication for the first row and third column: $0(1) + 1(2c) + 2(1) = 0 \implies 2c + 2 = 0 \implies 2c = -2 \implies c = -1$. Performing matrix multiplication for the third row and first column: $3(1) + a(-8) + 1(5) = 0 \implies 3 - 8a + 5 = 0 \implies 8 - 8a = 0 \implies 8a = 8 \implies a = 1$. Thus,the values are $a = 1$ and $c = -1$.

If $A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix}$ and $A^{-1} = \frac{1}{2} \begin{bmatrix} 1 & -1 & 1 \\ -8 & 6 & 2c \\ 5 & -3 & 1 \end{bmatrix}$,then the values of $a$ and $c$ are respectively:

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