If-a-matrix-A-is-such-that-3A-3-2A-2-5A-I-0-then-A-1-is-equal-to-

Question Number 70383 by ®Ëƒ ¬Ë°¹¾¨ ‰¦Í¦¿¨ ¸Ë¹Ç² last updated on 04/Oct/19

If a matrix A is such that 3 A^{3} + 2 A^{2} + 5 A + I = 0,

then A^{- 1} is equal to

Commented by mathmax by abdo last updated on 04/Oct/19

3 A^{3} + 2 A^{2} + 5 A + I = 0 \Rightarrow 3 A^{3} + 2 A^{2} + 5 A = - I \Rightarrow

A . (- 3 A^{2} - 2 A - 5 I) = I \Rightarrow A^{- 1} = - 3 A^{2} - 2 A - 5 I .