Question

If B is a $3\times 3$ matrix such that $B^2=0$, then det. $[(I+B{)}^{50}-50B]$ is equal to:

• A. 1
• B. 2
• C. 3
• D. 50

Answer 1

Answer: (A)

$\left[(1+B{)}^{50}-50B\right]=1+50B+\frac{50.49}{\lfloor 2}{B}^2+\dots \dots ..-50B$
$=1+B^2\{---------\}=1+0\{----------\}=1$