Question

Let $A =\begin{pmatrix}2 & -1 \\ 0 & 2\end{pmatrix}$. If $B = I -{ }^{5} C _{1}(\operatorname{adj} A )+{ }^{5} C _{2}$ $(\operatorname{adj} A)^{2}-\ldots-{ }^{5} C _{5}(\operatorname{adj} A )^{5}$, then the sum of all elements of the matrix $B$ is:

• A. -5
• B. -6
• C. -7
• D. -8

Answer 1

Answer: (C)

$B =( I -\operatorname{adj} A )^{5}=\begin{bmatrix}-1 & -1 \\0 & -1\end{bmatrix}^{5}=\begin{bmatrix}-1 & -5 \\0 & -1\end{bmatrix}$
Sum of its all elements $=-7$.