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If A satisfies the equation $x^3 -5x^2+4x+λ=0$, then $A^{-1}$ exists if |
$λ≠1$ $λ≠2$ $λ≠-1$ $λ≠0$ |
$λ≠0$ |
Since A satisfies the equation $x^3-5x^2+4x+λ=0$ $⇒A^3 -5A^2 + 4A + λI=0$ $⇒A (-A^2+5A-4 I) = λI$ $⇒A\left\{\frac{1}{λ}(-A^2+5A-4 I)\right\}=I$, if $λ≠0$ Hence, $A^{-1}$ exists and is equal to $\frac{1}{λ}(-A^2+5A-4 I)$ if $λ≠0$. |
