A is a square matrix of order 4, R (a) is equal to 4

A is a square matrix of order 4, R (a) is equal to 4

The relation between matrix A of order n and its adjoint matrix A * is as follows
If R (a) = n, then R (a *) = n
If R (a) = n-1, then R (a *) = 1
If R (a)

Let a * be the adjoint matrix of the third order square matrix A, if | a | = 2, then rank r (a *) =?

3. A * is also full rank
Because a is reversible, a * a = | a | e, that is to say, a is the inverse of a *, so a * is also full rank

Let a and a * be nonzero matrices of order n, where a * is the adjoint matrix of a and tangent AA * = 0, then what is the rank of a *,

Because AA * = |a|e
If AA * = 0, then | a | = 0
So r (a)