Perform matrix operations including addition, multiplication, determinant, inverse, and more with step-by-step solutions.
⎡1 0⎤
⎣0 1⎦
⎡cosθ -sinθ⎤
⎣sinθ cosθ⎦
⎡2 1⎤
⎣1 1⎦
⎡1 2⎤
⎣2 4⎦
Add corresponding elements of two matrices with same dimensions: A + B = [aᵢⱼ + bᵢⱼ]
Multiply matrices where columns of A equal rows of B: (AB)ᵢⱼ = Σ aᵢₖ × bₖⱼ
Scalar value from square matrix representing scaling factor and invertibility.
A⁻¹ such that A × A⁻¹ = I (identity matrix). Only exists if det(A) ≠ 0.
Flip matrix over its diagonal: (Aᵀ)ᵢⱼ = Aⱼᵢ. Rows become columns.
Multiply every element by a scalar: kA = [k × aᵢⱼ]. Scales the matrix.