a) Using elementary column transformation, compute the inverse of $\b…

Question

a) Using elementary column transformation, compute the inverse of $\begin{bmatrix} 1 & 2 & 5 \\ 3 & 1 & 4 \\ 1 & 1 & 2 \end{bmatrix}$.

b) Find all the eigen values of $A^3$ and $A+2I$, where $A = \begin{bmatrix} 2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2 \end{bmatrix}$.

c) If $\lambda$ is an eigen value of a square matrix, show that $\lambda^3$ is an eigen value of $A^3$.

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