TIFR-2019-Maths-B: 5

Question

True/False Question :

Suppose $A,B,C$ are $3\times3$ real matrices with Rank $A =2$, Rank $B=1$, Rank $C=2$. Then Rank $(ABC)=1$.

Answer 1

True

By the property:

Rank(AB) <= min(rank A, rank B)