Question

Let \(A\) be a \(4 \times 3\) real matrix with rank 2. Which one of the following statement is TRUE?
1. Rank of \({A^T}A\) is less than 2.
2. Rank of \({A^T}A\) is equal to 2.
3. Rank of \({A^T}A\) is greater than 2.
4. Rank of \({A^T}A\) can be any number between 1 and 3.

Answer 1

Correct Answer - Option 2 : Rank of \({A^T}A\) is equal to 2.

If \(A\) is real

rank of (\({A^T}\;A\)) = rank of \(A\) = rank of \({A^T}\) = rank of \(A{A^T}\)