answer this question
Answers
Question :
Let P and Q be 2×2 matrices ; consider the following statements
1) PQ=O⇒P=0 or Q = 0 or both
2) PQ = I ⇒ P =Q⁻¹
3)( P+ Q)² = P²+Q²+2PQ then
a. (1) and (3) are false while (2) is true
b. (2) and (3) are false while (1) is true
c.(1) and (2) are false while (3) is true
d.only (1) and (2) true
Theory:
A rectangular arrangements of numbers and Columbus is called a matrix .
Properties of Matrices :
1. Matrix multiplication :
a) (AB)C = A(BC)
b) (A+ B)² = A²+B²+AB+BA
c) if AB = 0
It does not mean that A = 0 or B = 0
Inverse of Matrix
If A and B are two matrices such that
AB = I = BA , then B is called the inverse of A denoted by A.
Solution :
Given : P& Q both matrices of order 2×2
we have to find correct options in the given Question .
1)PQ=O⇒P=0 or Q = 0 or both
⇒ It means both are zero matrix
2) PQ = I ⇒ P =Q⁻¹
⇒it means P is inverse of P or we can also say that Q is inverse of P
3) ( P+ Q)² = P²+Q²+2PQ
⇒ Generally Matrix multiplication is not commutative i.e PQ ≠QP
__________________________
After Analysing All options
corrects options are (1)&(2)
so the Answer option d)