A is a 4-square matrix and A 5 = 0. Then

Question

A is a 4-square matrix and A_5 (a raised to the power of 5) = 0. Then A_4 =

a) I

b) -I

c) 0

d) A

Answer 1

Question does not have any notion of  existing of inverse or related to rank. Therefore considering Zero matrix as A would satisfy all the constraints.

Therefore, (c) is the answer.

Answer 2

Should be C.

A^5 = A^4 * A =0

So one of A and A^4  determinant must be zero. (note am not saying zero matrix, none of them need to be that)

Suppose |A| $\neq$ 0

Then A^4 = 0

A^4 = A^3 * A =0

|A^3| should be 0.

A^3 = A^2 * A =0

|A^2| should be 0.

A^2 = A * A =0

|A| =0 but that make our initial assumption wrong.

So |A| = 0