Let \( A=\begin{bmatrix}2 & -1 \\ 0 & 2\end{bmatrix} \). If \( B=I-{}^{3}C_{1}(\mathrm{adj}\,A)+{}^{3}C_{2}(\mathrm{adj}\,A)^{2}-{}^{3}C_{3}(\mathrm{adj}\,A)^{3} \), then the sum of all elements of the matrix \( B \) is
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Matrix Tip:Identity matrix operations mimic scalar algebra rules. $I^n = I$ and $I \times A = A$. This allows us to use standard binomial theorem expansions on matrix polynomials safely.Memorize the $2\times2$ adjoint shortcut: swap the principal diagonal, negate the secondary diagonal.