Question

. (a) If A & B are non-zero square matrices of same order such that AB = A & BA = B then Prove that
A2= A & B2 = B.
(b) If A & B matrices such that
AB2= BA & A4 = I then prove that B16 = B & B15 = I.
(c) If A be a square Matrix such that
A16 + A8 = O, then show that
(A8 + A4+ I) – 1 = A8 - A4 + I

plsss someone helpppp class12 matrix

Answer 1

Hence proven that A^2 = A and B^2 = B

Step-by-step explanation:

Question statement:

If A & B are non-zero square matrices of same order such that AB = A & BA = B then Prove that  A2= A & B2 = B.

Solution:

AB = A

BA = B

X.Y = Y^x

A^2 = A.A= (AB)A = A(BA)   = BA (B)  = AB  = A

A^2 = A

B^2 = B.B = (BA)B   = B (AB)

B^2 = B.A = B

B^2 = B

Hence proven that A^2 = A and B^2 = B