Matrix Scalar Multiplication Calculator — Formula

## Scalar Multiplication of a Matrix

### Rule

**k × [[a, b], [c, d]] = [[ka, kb], [kc, kd]]**

Multiply every element by the scalar.

### Properties

- det(kA) = k^n × det(A) for an n×n matrix (k² × det for 2×2)
- Scalar multiplication distributes over addition: k(A + B) = kA + kB
- (jk)A = j(kA)

Esempio Risolto

Multiply [[1,2],[3,4]] by scalar 3.

  1. 3 × [[1,2],[3,4]] = [[3,6],[9,12]]
  2. Original det = 1×4 - 2×3 = -2
  3. New det = 9 × (-2) = -18 = 3² × (-2)