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If A = $\begin{bmatrix} -1 & 1 & 0 \\ 0 & 2 &-2 \\ 0& 0 & 3 \end{bmatrix}$ then trace of the matrix 3A+ adj A is ____

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$A =$ $\begin{bmatrix} -1 & 1 & 0 \\ 0 & 2 &-2 \\ 0& 0 & 3 \end{bmatrix}$

$A^2 =$ $\begin{bmatrix} 1 & 1 & -2 \\ 0 & 4 &-10 \\ 0& 0 & 9 \end{bmatrix}$

$adjA = $$\begin{bmatrix} 6 & 0 & 0 \\ -3 & -3 & 0 \\ -2& -2 & -2 \end{bmatrix}^T = $$\begin{bmatrix} 6 & -3 & -2 \\ 0 & -3 & -2 \\  0& 0 & -2 \end{bmatrix} $

$3A^2 + adj A = $ = $\begin{bmatrix} 3 & 3 & -6 \\ 0 & 12 &-30 \\ 0& 0 & 27 \end{bmatrix} + $$\begin{bmatrix} 6 & -3 & -2\\ 0 & -3 & -2 \\  0& 0 & -2 \end{bmatrix} $ = $\begin{bmatrix} 9 & 0 & -8 \\ 0 & 9 & -32 \\  0& 0 & 25 \end{bmatrix} $

Trace = $9 + 9 + 25 = 43$
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