Matrix operations are the basic of deep learning, we will list some laws of matrix operations in this tutorial, these laws may help us to simply the computation of formulas.

**A, B, C are matrix**

(1) A + B = B+ A

(2) A + (B + C) = (A + B) + C

(3) A * (B * C) = (A * B) * C = A * B * C

(4) A * (B + C) = A * B + A * C

(5) (A + B) * C = A * C + B * C

(6) k * (A + B) = k * A + k *B, k is a scalar

(7) A * I = I * A = A, I is identity matrix

(8) A^{p}= A*A*A*⋯*A (p factors )

(9) (A^{p})*(A^{q}) = A^{p+q}

(10) (A^{p})^{q }= A^{pq}

(11) AB ≠ BA