A matrix A has 3 rows, and the matrix \(A'A\) has 25 elements, where \(A'\) is the transpose of A. The number of elements in A is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 15
Let A be of order \(3 \times n\). Then \(A'\) is of order \(n \times 3\), and
\(A'A\) is of order \(n \times n\)
\(A'A\) has 25 elements, so
\(n^2 = 25\)
\(n = 5\)
So A is of order \(3 \times 5\), and the number of elements in A is
\(3 \times 5 = 15\)