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Algebra Level 4

Given that A A is a matrix of order 5 × 3 5\times3 and B B is a matrix of order 3 × 5 3\times5 , then what can be said about ∣ C ∣ |C| if it's given that A × B = C A×B=C ?

> 0 >0 Can't be determined. < 0 <0 0 0

Akshat Sharda by Akshat Sharda , 21, India

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2 solutions

Shourya Pandey
Jun 3, 2017

Let R ( X ) R(X) denote the rank of a matrix X X . Then

R ( C ) ≤ m i n ( R ( A ) , R ( B ) ) ≤ m i n ( 3 , 3 ) = 3 R(C) \leq min(R(A), R(B)) \leq min(3,3) = 3 , but C C is a 5 × 5 5 \times 5 matrix. So its determinant must be 0 0 ( a square matrix with a non-zero determinant has its rank equal to its order).

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Prakhar Bindal
May 29, 2017

Use the concept of rank of matrix

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you explain ?

Aditya Sky - 4 years ago

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