Show that the matrix A is non-singular for all real values of a

Given: A = [a -5; 2 a+4]. 1) First find the determinant of A using the known formula => det A = a²+ 4a + 10. A singular matrix is one in which it's determinant equals zero (the determinant of a matrix is a number that captures information about the characteristics of the matrix). The roots of the quadratic are complex, so the graph never equals zero/ no real roots. Therefore it must be a non-singular matrix.