?Develop a Cayley-Hamilton formula for the inverse of a 2 ? 2 matrix, and apply it to

Chapter 5, Problem 69

(choose chapter or problem)

Develop a Cayley-Hamilton formula for the inverse of a 2 ⨉ 2 matrix, and apply it to compute the inverses of the following.

(a) $\left[\begin{array}{rr} 3 & 2 \\ -2 & -3 \end{array}\right]$

(b) $\left[\begin{array}{rr} 3 & 5 \\ -1 & -1 \end{array}\right]$

Equation Transcription:

$\left[{{\ }_{-2\ \ \ \ \ \ \ \ \ \ \ \ -3}^{\ \ 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ 2}}\right]$

$\left[{{\ }_{-1\ \ \ \ \ \ \ \ \ \ \ \ \ \ -1}^{\ \ \ 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5}}\right]$

Text Transcription:

[3 2 _ -2 -3]

[3 5 _ -1 -1]

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