Question 1

When is a matrix invertible (non-singular)?

Accepted Answer

A square matrix is invertible if and only if its determinant is non-zero (det(A) ≠ 0). Singular matrices with det(A) = 0 cannot be inverted because dividing by zero determinant is undefined.

Question 2

What is matrix multiplication row-by-column rule?

Accepted Answer

To compute element C[i, j] in C = AB, compute the dot product of row i from Matrix A with column j from Matrix B: C[i,j] = Σ A[i,k] × B[k,j].

Question 3

What does the Determinant geometrically represent?

Accepted Answer

In 2×2, det(A) is the signed area scaling factor of the parallelogram spanned by basis vectors. In 3×3, det(A) is the signed volume of the parallelepiped.

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