If A - - 1 -1 1- 2 -1 0- 1 0 0 -Find A2 and show that A2 - A-1

A^2 = AA = [ #160; #160; #160; #160; #160; #160; #160; 0 amp; 0 amp; 1; #160; #160; #160; #160; #160; #160; #160; 0 amp; 1 amp; ...

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Inverse of a Matrix

If A = [ 1 ...

Question

If A = $⎡ ⎢ ⎢ ⎣ \begin{matrix} 1 & - 1 & 1 2 & - 1 & 0 1 & 0 & 0 \end{matrix} ⎤ ⎥ ⎥ ⎦$
Find $A^{2}$ and show that $A^{2} = A^{- 1}$

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Solution

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A = ⎡ ⎢ ⎣ \begin{matrix} 1 & - 1 & 1 2 & - 1 & 0 1 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 2 2 & 1 & 2 2 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦

A^{2} - 4 A - 5 I = 0

A^{- 1}

A = [\begin{matrix} - 1 & 2 & 0 \\ - 1 & 1 & 1 \\ 0 & 1 & 0 \end{matrix}]

A^{2} = A^{- 1} .

A = ⎡ ⎢ ⎣ \begin{matrix} - 1 & 2 & 0 - 1 & 1 & 1 0 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦

A^{2} = A^{- 1}

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & - 1 & 1 2 & - 1 & 0 1 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦,

A^{3} = I

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