Correct Answer - Option 4 : Symmetric Matrix

**Concept:**

Transpose of matrix A = A^{T}

Let Product of matrix and its transpose = AA^{T} = B

Now, transpose of matrix B, B^{T} = (AA^{T})^{T}

B^{T}= (A^{T})^{T} (A^{T}) {Since, (PQ)^{T} = Q^{T}P^{T}}

B^{T}= AA^{T} = B

Since, (AA^{T})^{T} = AA^{T}, hence it is a symmetric matrix.

Therefore, the product of a matrix and its transpose will always be a symmetric matrix.