Question: 12. If A is defined below, find a 4 x 4 matrix B such that tr (AB) = rank (A). $$ A = begin{bmatrix} 3

12. If A is defined below, find a 4 x 4 matrix B such that tr (AB) = rank (A).

$$

A =

\begin{bmatrix}

3 & 1 & -2 & 0 \\

1 & 2 & 3 & -1 \\

-2 & 1 & 3 & 4 \\

6 & 2 & -2 & -2

\end{bmatrix}

$$

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