﻿ 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 : Kaysons Education

# 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

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## Question

### 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

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