If A = \left(\right. 2 & 2 \\ 9 & 4 \left.\right) and \textrm{ }\textrm{ } I = \left(\right. 1 & 0 \\ 0 & 1 \left.\right), then 10A

Engineering

Mathematics

Inverse of a Matrix

Question

If $A = (\begin{matrix} 2 & 2 \\ 9 & 4 \end{matrix}) and I = (\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix})$ , then 10A^–1 is equal to :

4I – A

A – 4I

6I – A

A –6I

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Characteristics equation of matrix ‘A’ is

$| \begin{matrix} 2 - x & 2 \\ 9 & 4 - x \end{matrix} | = 0 \Rightarrow x^{2} - 6 x - 10 = 0$

$∴$ A² – 6A – 10 I = 0

⇒ 10A^–1 = A – 6I