You visited us 1 times! Enjoying our articles? Unlock Full Access!

Combination

If A is a nil...

Question

If $A$ is a nilpotent matrix of index $2,$ then for any positive integer $n, A (I + A)^{n}$ is equal to

A^{- 1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

A^{n}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

I_{n}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $A$
Given that $A$ is a nilpotent matrix of index $2$
$A^{2} = O, A^{3} = A^{4} = \dots = A^{n} = O$

Then, $A (I + A)^{n} = A (I + n A) = A + n A^{2} = A$

Suggest Corrections

Similar questions

A

2

n

A (I + A)^{n}

A

| A | = 2

n, | A^{n} |

(\begin{matrix} 2 & 4 - 1 & k \end{matrix})

2,

k

r

r

A^{r} = 0

A

B

A + B

A^{m} = 0

(I - A)^{n} = I + A + A^{2} + A^{3} + . . . . + A^{m - 1}

Join BYJU'S Learning Program

Explore more

Join BYJU'S Learning Program