Matrix Operations and Multiplication

A matrix is a rectangular array of numbers arranged in rows and columns.

To add two matrices, they must have the same dimensions, and you add corresponding elements.

A + B = [[1+5, 2+6], [3+7, 4+8]] = [[6, 8], [10, 12]]

Matrix multiplication involves taking the dot product of rows and columns from two matrices.

The number of columns in the first matrix must equal the number of rows in the second matrix.

Matrix B must be a 3xN matrix, where N can be any positive integer.

A * B = [[1*7 + 2*9 + 3*11, 1*8 + 2*10 + 3*12], [4*7 + 5*9 + 6*11, 4*8 + 5*10 + 6*12]] = [[58, 64], [139, 154]]

An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.

A zero matrix is a matrix in which all elements are zero.

To subtract two matrices, they must have the same dimensions, and you subtract corresponding elements.