if AB=A and BA=B then which is correct a) A^2=A b) B^2=B c)A=I d) B=I? chapter matrices

Question

maheshchary · Answer

C

Nikhil Upadhyay · Answer

Both options (a) and (b) are correct .A 2 =A & B 2 =B.

rajnish kumar · Answer

Nikhil Upadhyay but why C and D not correct??? if we multiply both side by A inverse.... we will get A=I. ???

Nikhil Upadhyay · Answer

Look options a) and b) are correct showing that options c and d are also correct.see below for explaination. A 2 =A--------->A.A=A------------->A=A -1 .A(taking one of the A to right side so it became A inverse) But (A -1 .A=I) Therefore A=I.Similarily B=I.Thus option a and b are correct implementing options c and d.

rajnish kumar · Answer

i am getting you. but in the book answer is only a and b. so i am confused.

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if AB=A and BA=B then which is correct a) A^2=A b) B^2=B c)A=I d) B=I? chapter matrices

if AB=A and BA=B then which is correct a) A^2=A b) B^2=B c)A=I d) B=I? chapter matrices

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if AB=A and BA=B then which is correct a) A^2=A b) B^2=B c)A=I d) B=I? chapter matrices

if AB=A and BA=B then which is correct a) A^2=A b) B^2=B c)A=I d) B=I? chapter matrices

5 Answers

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