" If "A=[[8,-6,2],[-6,7,-4],[2,-4,3]]," then "A(A-3I)(A-15I)

If A=[{:(8,-6,2),(-6,7,-4),(2,-4,3):}] verify that A(adjA)=(adjA)A=A|A|I_(3) .

If A+2I= [(6,2),(3,-4)] ,then A(A+I)=

If A={1,2,3,4,5,6,7,8} and B={1,3,4,6,7,8,9} then

If U ={1,2,3, 4,5,6,7,8} and A={2,4,6,8} , Find (i) A' (ii) (A')' .

Prove that the value of the determinant |[-7, 5+3i,2/3-4i], [5-3i,8, 4+5i], [2/3+4i,4-5i,9]| is real.

State with reason whether following functions have inverse (i) f:{1,2,3,4} ->{10}" "w i t h" "f={(1, 10),(2, 10),(3, 10),(4, 10)} (ii) g:{5," "6," "7," "8}->{1,2,3,4}" "w i t h" "g={(5," "4),(6," "3),(7," "4),(8," "2)} (iii) h :{2,3,4,5} ->{7,9

Wherever possible write each of the following as a single matrix. (i) [{:(,1,2),(,3,4):}]+[{:(,-1,-2),(,1,-7):}] (ii) [{:(,2,3,4),(,5,6,7):}]-[{:(,0,2,3),(,6,-1,0):}] (iii) [{:(,0,1,2),(,4,6,7):}]+[{:(,3,4),(,6,8):}]

If z = |{:(-5,3+4i,5-7i),(3-4i,6,8+7i),(5+7i,8-7i,9):}| , then z is

If U= {1,2,3,4,5,6,7,8,9}, A= {2,4,6,8}, B {2,3,5,7} . Verify that : (i) (AuuB)=AcapB .