Question

If A is a non-zero column matrix of order $m\times 1$ and B is a non-zero row matrix of order $1\times n$ then rank of AB equals ?

• A. m
• B. n
• C. 1
• D. none of these

Answer 1

Answer: (C)

1

Since, order of matrix A is $m\times 1$
Rank of $A\le min$ $m,1$
Rank of A is $1$.
Since, order of matrix B is $1\times n$
Rank of $B\le min1,n$
Rank of B is $1$.
Now, rank of product of matrices is not greater than rank of both matrices.
Therefore, rank of $AB=1$
Hence, option 'C' is correct.