MatricesEasy
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.
A2 - B2 = A2 + AB - BA - B2
⇒ AB = BA.
Create a free account to view solution
View Solution FreeMore Matrices Questions
If A and B are square matrices of same orders, then adj (AB) equals -...If A and B are square matrices of same order, then which of the following is skew- symmetric-...Let $A = \begin{bmatrix} 1 & 1 & 2 \\ - 2 & 0 & 1 \\ 1 & 3 & 5 \end{bmatrix}$. Then the sum of a...If A = , then |A +AT| equals -...If A = , then (adj A)23 is equal to -...