MatricesHard

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 ?

Options

A.A = B
B.AB = BA
C.either of A or B is a zero matrix
D.either of A or B is an identity matrix

Solution

A2 - B2 = (A - B) (A + B)
A2 - B2 = A2 + AB - BA - B2
⇒ AB = BA.

Create a free account to view solution

View Solution Free
Topic: Matrices·Practice all Matrices questions

More Matrices Questions

For suitable matrices A, B; the false statement is-...If A = and f(x) = 2x2 − 3x, then f(A) equals -...If A be a matrix such that inverse of 7A is the matrix , then A equals -...If A is a matrix of order 3 × 4, then both ABT and BTA are defined if order of B is -...The inverse matrix of is -...