Question

For which values of a does ????8 a
a 2
???? have an inverse matrix?

Answer 1

a not equal to 4 and -4.

Explanation:

As we know the inverse of a matrix is adj(A)/det(A).

|A|=8*2-a*a

|A|=16-a²

For the inverse to exists the determinant should be non-zero,|A|≠0.

16-a²≠0

(4-a)(4+a)≠0

4-a≠0 and 4+a≠0

a≠4 and a≠-4.

Hence the inverse of the matrix will exists if the values of a are not equal to 4 and -4.