matrix properties

Question

If A and B are symmetric matrices of the same order, then AB is symmetric if

RankGuru · Accepted Answer

1. **Symmetric Constraint**: We require $(AB)^T = AB$.
2. **Transpose Property**: Note that $(AB)^T = B^T A^T$.
3. **Application**: Since $A$ and $B$ are symmetric, $A^T = A$ and $B^T = B$.
   - Substituting: $(AB)^T = B \, A$.
4. **Equivalence**: For $B \, A$ to equal $A \, B$, the matrices must **commute ($AB = BA$)**. If they don't commute, the product is not symmetric.

Rank Guru

matrix properties

Select the correct option:

More matrix properties Practice Questions

The trace of a square matrix A is defined as the sum of its diagonal elements. If A = [[1, 2, 3], [4...

If A is a skew-symmetric matrix of odd order, then |A| equals