If a Matrix a is Such that 3 a 3 + 2 a 2 + 5 a + I = 0 , Then a − 1 Equal to - Mathematics

Question

If a matrix A is such that \[3A^3 + 2 A^2 + 5 A + I = 0,\text{ then }A^{- 1}\] equal to _______________ .

Options

\[- \left( 3 A^2 + 2 A + 5 \right)\]
\[3 A^2 + 2 A + 5\]
\[3 A^2 - 2 A - 5\]
none of these

MCQ

Solution

None of these

\[3 A^3 + 2 A^2 + 5A + I = 0\]

\[ \Rightarrow 3 A^3 + 2 A^2 + 5A = - I\]

\[ \Rightarrow A^{- 1} (3 A^3 + 2 A^2 + 5A) = - I A^{- 1} \]

\[ \Rightarrow 3 A^2 + 2A + 5I = - A^{- 1} \]

\[ \Rightarrow A^{- 1} = - 3 A^2 - 2A - 5I\]

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Properties of Matrix Multiplication - Inverse of a Square Matrix by the Adjoint Method

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Q 28 Q 27 Q 29

Chapter 7: Adjoint and Inverse of a Matrix - Exercise 7.4 [Page 39]

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RD Sharma Mathematics [English] Class 12

Chapter 7 Adjoint and Inverse of a Matrix
Exercise 7.4 | Q 28 | Page 39

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