Multiplying Matrices

Scalar matrix multiplications
Distribute the outside number for all the numbers on the inside.

When multiplying matrices. We must note that the dimensions are to be similar. The colums of the 1st matrix and the rows of the 2nd matrix must be equal. Then use the outer dimensions as the product matrix. So...
If we multiply a 2×3 matrix with a 3×1 matrix, the product matrix is 2×1

Here is how we get M₁₁ and M₂₂ in the product.

M₁₁ = r₁₁× t₁₁  +  r₁₂× t₂₁  +   r₁₃×t₃₁
M₁₂