If `A` and `B` are non-singular matrices of the same order, write whether `A B` is singular or non-singular.

Explanation

To determine whether the product of two non-singular matrices \( A \) and \( B \) is singular or non-singular, we can follow these steps:

### Step 1: Understand the definition of non-singular matrices
A matrix is non-singular if its determinant is not equal to zero. Therefore, for matrices \( A \) and \( B \):
\[ \text{det}(A) \neq 0 \quad \text{and} \quad \text{det}(B) \neq 0 \]

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