What is matrix multiplication?

Matrix multiplication combines rows of the first matrix with columns of the second. Element (i,j) = sum of products of row i and column j.

What is a determinant?

The determinant is a scalar value computed from matrix elements. For 2×2: det(A) = ad-bc. It indicates matrix invertibility.

Element-wise multiplies corresponding elements. Matrix multiplication uses the dot product rule.

Free matrix calculator. Perform matrix addition, subtraction, multiplication, and determinant calculations for 2×2 and 3×3 matrices.

Add, subtract, multiply 2×2 and 3×3 matrices, calculate determinants.

det (A) = a d - b c (2\times2); expansion by minors (3\times3)