𝑆𝑢𝑝𝑝𝑜𝑠𝑒 𝑡ℎ𝑎𝑡 𝑡ℎ𝑒 𝑐ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐 𝑝𝑜𝑙𝑦𝑛𝑜𝑚𝑖𝑎𝑙 𝑜𝑓 𝑠𝑜𝑚𝑒 𝑚𝑎𝑡𝑟𝑖𝑥 𝐴 𝑖𝑠 𝑓𝑜𝑢𝑛𝑑 𝑡𝑜 𝑏𝑒 𝑝(𝜆) = (𝜆 - 1)𝜆 -32  𝜆 -43  . 𝑊ℎ𝑎𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑖𝑧𝑒 𝑜𝑓 𝐴?

The characteristic polynomial of a matrix is given by the determinant of (λI - A), where I is the identity matrix, A is the matrix in question, and λ are the eigenvalues. The degree of this polynomial is equal to the size of the matrix.

In the given polynomial p(λ) = (λ - 1)λ -32 λ -43, we can see that the highest power of λ is 3. Therefore, the size of the matrix A is 3x3.