For integers x, y, define x ⊕ y = x ⋅ y + 1; read "x plus y" where x ⋅ y is defined normally.
a. is this form of addition commutative? explain why or why not.
b. is this form of addition associative? explain why or why not.

To diagonalize an nxn matrix a means to find an invertible matrix p and a diagonal matrix d such that a pdp d p ap or [1 3 dh epap 3 let a=-3 -5 -3 3 3 1 step 1: find the eigenvalues of matrix a "2's" step 2: find the corresponding eigenvectors of a step 3: createp from eigenvectors in step 2 step 4 create d with matching eigenvalues.