To compute C from A*C multiply A*C by A inverse on the left C = A^(-1)*A*C = (A^(-1)*A)*C = I*C = C Since matrix multiplication is not abelian, A*C*A^(-1) gives the wrong answer (most of the time). Determinates. Expansion by minors, special case for n = 1, 2, special case for lots of zeros, special case using A(i,:)= A(i,:)+c*A(j,:). Do not use special 3x3 method. Solving systems in upper triangular form. A is nilpotent if A not= 0, but eventually A^2, A^3, A^4, ... is the zero matrix.