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Answers to the exercises are available here.

Exercise 1

If
M=matrix(c(1:10),nrow=5,ncol=2, dimnames=list(c('a','b','c','d','e'),c('A','B')))

What is the value of: M

Exercise 2

Consider the matrix M,
What is the value of:
M[1,]
M[,1]
M[3,2]
M['e','A']

Exercise 3

Consider the matrix N
N=matrix(c(1:9),nrow=3,ncol=3, dimnames=list(c('a','b','c'),c('A','B','C'))) 
What is the value of: diag(N)

Exercise 4

What is the value of: diag(4,3,3)
Is matrix ?

Exercise 5

If M=matrix(c(1:9),3,3,byrow=T, dimnames=list(c('a','b','c'),c('d','e','f')))
What is the value of:
rownames(M)
colnames(M)

Exercise 6

What is the value of:
upper.tri(M)
lower.tri(M)
lower.tri(M,diag=T)

Exercise 7

Consider two matrix,
M,N 
M=matrix(c(1:9),3,3,byrow=T)
N=matrix(c(1:9),3,3) 
What is the value of:

M*N 

Exercise 8

Consider two matrix,
M,N 
M=matrix(c(1:9),3,3,byrow=T)
N=matrix(c(1:9),3,3) 
What is the value of:

M%*%N 

Exercise 9

Consider two matrix,
M,N 
M=matrix(c(1:9),3,3,byrow=T)
N=matrix(c(1:9),3,3) 

What is the value of:

(M+N)^2

Exercise 10
Consider two matrix,
M,N 
M=matrix(c(1:9),3,3,byrow=T)
N=matrix(c(1:9),3,3) 

What is the value of:

M/N

Want to practice matrices a bit more? We have more exercise sets on this topic here.