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

Integration Using Substitution

If a matrix A...

Question

If a matrix A is such that $3 A^{3} + 2 A^{2} + 5 A + I = 0$ , then $A^{- 1}$ is equal to

- (3 A^{2} + 2 A + 5)

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

3 A^{2} + 2 A + 5

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

3 A^{2} - 2 A - 5

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

none of these

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

Open in App

Solution

The correct option is B $- (3 A^{2} + 2 A + 5)$
Given, $3 A^{3} + 2 A^{2} + 5 A + I = O$
$\Rightarrow 3 A^{3} A^{- 1} + 2 A^{2} A^{- 1} + 5 A A^{- 1} + I A^{- 1} = O$
$\Rightarrow 3 A^{2} + 2 A + 5 I + A^{- 1} = O$
$\Rightarrow A^{- 1} = - (3 A^{2} + 2 A + 5 I)$
Hence, option 'A' is correct.

Suggest Corrections

Similar questions

A^{3} + 2 A^{2} + 5 A + I = 0, then A^{- 1}

- (3 A^{2} + 2 A + 5)

3 A^{2} + 2 A + 5

3 A^{2} - 2 A - 5

5 - (3 a^{2} - 2 a) (6 - 3 a^{2} + 2 a)

\frac{2 a^{2} - 3 a - 2}{a^{2} - a - 6} \div \frac{3 a^{2} - 5 a - 2}{3 a^{2} - 8 a - 3}

\frac{2 a + 1}{a - 2}

1

0

(a^{2} - 2 a + 3) (a^{2} - 2 a + 5) - 35

5 - (3 a^{2} - 2 a) (6 - 3 a^{2} + 2 a)

Join BYJU'S Learning Program