Question

If A is Square Matrix of order 3, then product of A and its transpose is
1. Unit Matrix
2. Zero Matrix
3. Identity Matrix
4. Symmetric Matrix 

Answer 1

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^TP^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.