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We are given the matrix: $$ A = \begin{bmatrix} 1 & -1 \\ 0 & 2 \end{bmatrix} $$ We need to verify the Cayley-Hamilton theorem, which states that every square matrix satisfies its own characteristic equation. --- ### Step 1: Find the characteristic polynomial The characteristic polynomial of matrix $A$ is given by: $$ \text{det}(A - \lambda I) = 0 $$ So, $$ A - \lambda I = \begin{bmatrix} 1 - \lambda & -1 \\ 0 & 2 - \lambda \end{bmatrix} $$ Now calculate the determinant: $$ \text{det}(A - \lambda I) = (1 - ____ _____ _________ ____ ______ _________ _______ _______ ____ __________ _____ ____.
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