C22 : Compute the product AB of the two matrices below using both the definition of the matrix-vector product and the definition of matrix multiplication.

A = matrix(c(1, 0, -2, 1), byrow = T, nrow = 2)
B = matrix(c(2, 3, 4, 6), byrow = T, nrow = 2)

#Multiplication using matrix-vector product
(AB.1 <- B[1,1] * A[,1] + B[2,1] * A[,2])

## [1] 2 0

(AB.2 <- B[1,2] * A[,1] + B[2,2] * A[,2])

## [1] 3 0

(AB <- cbind(AB.1, AB.2))

##      AB.1 AB.2
## [1,]    2    3
## [2,]    0    0

#Multiplication using matrix multiplication
(AB.1.1 <- A[1,1] * B[1,1] + A[1,2] * B[2,1])

## [1] 2

(AB.2.1 <- A[2,1] * B[1,1] + A[2,2] * B[2,1])

## [1] 0

(AB.1.2 <- A[1,1] * B[1,2] + A[1,2] * B[2,2])

## [1] 3

(AB.2.2 <- A[2,1] * B[1,2] + A[2,2] * B[2,2])

## [1] 0

(AB <- matrix(c(AB.1.1, AB.2.1, AB.1.2, AB.2.2), nrow = 2, byrow = F))

##      [,1] [,2]
## [1,]    2    3
## [2,]    0    0