Prove that tha matrix `A[(a,b),(c,d)]` satisfies the relation `A^2-A(a+d)+(ad-bc)I=0` where is a unit matrix of order two.

Prove that tha matrix A[[a,bc,d]] satisfies the relation A^(2)-A(a+d)+(ad-bc)I=0 where is a unit matrix of order two.

Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc) I=0 where I is the 2 x 2 unit matrix.

Given that matrix B = [{:( a,b),(c,d) :}] find lambda so that B^(2) - ( a+d) B =lambda l. where I is a unit matrix of order 2.

A skew symmetric matrix S satisfies the relations S^(2)+1=0 where I is a unit matrix then SS' is equal to

A skew symmetric matrix S satisfies the rotation S^(2) +I=0 ,where I is a unit matrix , Show that S S^T =I

If a, b, c, d in R and A=[(a,b),(c,d)] , show that A^2-(a+d)A+(ad-bc)I is a null matrix.

A skew - symmetric matrix S satisfies the relation S^(2) + I = 0 , where I is a unit matrix , then S is a)Idempotent b)Orthogonal c)Involuntary d)None of these