Let A = ( cc 2 & -1 0 & 2 ). If B = I - ^ 5 C _ 1 (adj A )+ ^ 5 C… - Vidyadip

MCQ

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

A
$-5$
B
$-6$
✓
$-7$
D
$-8$

✓

Answer

Correct option: C.

$-7$

c
$B =( I -\operatorname{adjA})^{5}=\left[\begin{array}{cc} -1 & -1 \\ 0 & -1 \end{array}\right]^{5}=\left[\begin{array}{cc} -1 & -5 \\ 0 & -1 \end{array}\right]$

Sum of its all elements $=-7$.

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