📘 Question
If \(A\) is a square matrix, then \(AA’\) (or \(A A^T\)) is:
(a) skew-symmetric matrix
(b) symmetric matrix
(c) diagonal matrix
(d) none of these
✏️ Step-by-Step Solution
Step 1: Use transpose property
\[
(AA^T)^T = (A^T)^T A^T
\]
Step 2: Simplify
\[
= A A^T
\]
Step 3: Conclusion
Since:
\[
(AA^T)^T = AA^T
\]
Therefore, \(AA^T\) is a symmetric matrix.
✅ Final Answer
\[
\boxed{(b)\; \text{symmetric matrix}}
\]
💡 Key Concept
A matrix is symmetric if \(A^T = A\). Here, \(AA^T\) always satisfies this condition.