2x2 Scalar Matrix Multiplication Calculator

About this calculator

Scalar multiplication of a matrix is the simplest matrix operation: every single entry of the matrix is multiplied by the same number, called the scalar. For a 2×2 matrix with entries a, b, c, d, multiplying by scalar k gives a new 2×2 matrix with entries ka, kb, kc, kd — the matrix's shape never changes, only the size of every value inside it.

This operation is a building block for almost everything else done with matrices: scaling a matrix by a constant shows up when uniformly resizing a shape in computer graphics, adjusting the magnitude of a physical quantity represented as a matrix in physics and engineering, and combining scalar multiplication with matrix addition and multiplication is exactly how linear algebra courses introduce the vector space structure that matrices form.

Enter a scalar value and the four entries of a 2×2 matrix, and the calculator multiplies every entry by the scalar and returns the resulting matrix.