Two matrices can only be added if they have the same dimensions. Add them entry by entry:
[acbd]+[egfh]=[a+ec+gb+fd+h]
Multiplication
Two matrices can be multiplied when the number of columns in the first equals the number of rows in the second. Each entry of the product is the sum of the products of the corresponding row (from the first matrix) and column (from the second matrix).
Worked example
Given:
A=0−6760−8780,B=011102120,C=2−23
Calculate AB and AC. (Note: B is 3×3 and C is 3×1, so B+C isn't a defined matrix operation, only AB and AC are computed here.)
AB: multiplying each row of A by each column of B gives
AB=138−81410712−6−9
AC: multiplying each row of A by the column C gives
Matrices and quadratic equations are both core algebra topics worth having side by side as you build up your algebra toolkit. Recognizing special matrix shapes and their properties builds directly on the addition and multiplication covered here.