Matrices

Question

If A and B are square matrices of size n × n such that A2 − B2 = (A − B) (A + B), then which of the following will be always true?

  • A = B

  • AB = BA

  • either of A or B is a zero matrix

  • either of A or B is an identity matrix

Answer

B.

AB = BA

A2 − B2 = (A − B) (A + B)
A2 − B2 = A2 + AB − BA − B2
⇒ AB = BA

Sponsor Area

Some More Questions From Matrices Chapter