Question 1: Given , , and that , find the value of .

Answer:

Similarly,

and

Hence

Question 2: If , and , then find:

i) ii)

Also find if

Answer:

i)

ii)

Therefore

Question 3: Given , and , find

i) ii) . Find whether

Answer:

i)

ii)

Therefore

Question 4: If , and , find i) ii). Are these equal.

Answer:

i)

ii)

Question 5: If , , find matrix such that .

Answer:

Let

Therefore

Solving the above two equations

Question 6: If , find

Answer:

Question 7: If , find i) ii)

Answer:

Therefore

i)

ii)

Question 8: If , show that ; where is a unit matrix.

Answer:

LHS

LHS = RHS. Hence proven.

Question 9: If , , find such that .

Answer:

Therefore

Therefore

Hence

Question 10: Evaluate .

Answer:

.

Question 11: State True or False with reason

Answer:

i) : True > addition of matrices is commutative

ii) : False > subtraction of matrices is not commutative

iii) : True > Multiplication of matrices is associative

iv) : True > Multiplication of matrices is distributive over addition

v) : True > Multiplication of matrices is distributive over subtraction

vi) : True > Multiplication of matrices is distributive over subtraction

vii) : False > Laws of algebra for factorization is not applicable to matrices

viii) : False > Laws of algebra for factorization is not applicable to matrices