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

- a)- (3 A
^{2}+ 2 A + 5I) - b)3 A
^{2}+ 2 A + 5I - c)- 3 A
^{2}- 2 A - 5 - d)none of these

Correct answer is option 'C'. Can you explain this answer?

Dronacharya Institute
Aug 28, 2021 |

3A^{3 }+ 2A^{2 }+ 5A + I = 0

3A^{3 }+ 2A^{2 }+ 5A + AA^{−1 }= 0

A^{−1 }= −3A^{2 }− 2A − 5

3A

A

3A3+ 2A2+ 5A + I = 03A3+ 2A2+ 5A + AA−1= 0A−1= −3A2− 2A − 5

3A3+ 2A2+ 5A + I = 03A3+ 2A2+ 5A + AA−1= 0A−1= −3A2− 2A − 5