Let A be an n×n matrix such that A^4=I_n and let M=A^3+A^2+A+I_n.

a)   Show that  is non-singular.

Considering the given conditions for the n x n matrix, it gives,

Q‒2. Find all values of  for which the following linear system has (i) no solution, (ii) a unique solution, (iii) infinitely many solutions:

Q‒3. Let 

a)   Find all values of  for which  is singular.

Q‒4. A. Let  and  be two skew-symmetric  matrices. Show that  is a scalar matrix.

Consider two matrices that are A and B and they commute each other in the two square diagonal matrices of order 2

a)   Let  and  be two   matrices satisfying. Show that  is a symmetric matrix and  is a skew-symmetric matrix.

As we know that a skew symmetric matrix is a matric whose transpose is equal to the negative of the same matrix and the condition below, satisfies for the skew symmetric matrix.