Question

Let A and B be two 2 × 2 matrices. Consider the statements   

(i) AB = O ⇒ A = O or B = O    

(ii) AB = I2 ⇒ A = B–1    

(iii) (A + B)2 = A2 + 2AB + B2.  

Then

Solution

Correct option is

(i) and (iii) are false, (ii) is true

(i) is false. 

          

        

Thus,   AB = O but neither A = O nor B = O    

(iii) is false since matrix multiplication is not commutative.  

(ii) is true at the product AB is an indentify matrix, if and only B is inverse of the matrix A.

SIMILAR QUESTIONS

Q1

, then value of α for which A2 = B is

Q2
Q3
Q4

Let A, B be two n × n matrix such that A + B = AB, then

Q5

If A and B are symmetric matrices, then AB – BA is a

Q6

The inverse of a symmetric matrix (if it exists) is

Q7

The inverse of a skew symmetric matrix (if it exists) is

Q8

The inverse of a skew symmetric matrix of odd order is

Q9

If A is an orthogonal matrix, then |A| is

Q10

If A is a non-singular matrix of size 3 × 3, then adj (adj A) is equal to