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  • How to solve this problem- If B is a 3x3 matrix such that B2=0, then det. [ (I + B)50 - 50B] is equal to :

 If B is a 3x3 matrix such that B2=0, then det. [ (I + B)50 - 50B] is equal to :

  • Option 1)

    1

  • Option 2)

    2

  • Option 3)

    3

  • Option 4)

    50

 

Answers (1)

As we learnt in 

Multiplication of matrices -

-

 

Since B^{2}=0 so that B= \begin{vmatrix} 0 &\alpha \\ 0&0 \end{vmatrix} (det)

 

\Rightarrow Now \left ( B+I \right )^{50} = I+50\beta

\Rightarrow \left ( I+\beta \right )^{50}- 50\beta=I

\therefore det\left [ \left ( I+\beta \right )^{50}-50\beta \right ]

= det\left ( I \right )=1

 


Option 1)

1

This option is correct.

Option 2)

2

This option is incorrect.

Option 3)

3

This option is incorrect.

Option 4)

50

This option is incorrect.

Posted by

Sabhrant Ambastha

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