**Question 1 :**

If

then find AB and BA. Are they equal ?

**Question 2 :**

If

verify (AB)C = A(BC).

**Question 3 :**

If

verify that (AB)^{T} = B^{T}A^{T }

**Question 4 :**

Prove that

are inverse to each other under matrix multiplication.

**Question 5 :**

If

find (A + B)C and AC + BC. Is (A + B)C = AC + BC ?

**Question 6 :**

If A and B are square matrices such that

AB = I and BA = I

then B is

(A) Unit matrix

(B) Null matrix

(C) Multiplicative inverse matrix of A

(D) -A

**Question 1 :**

If

then find AB and BA. Are they equal ?

**Solution :**

AB and BA are not equal.

**Question 2 :**

If

verify (AB)C = A(BC).

**Solution :**

Associative property is true in matrix multiplication.

**Question 3 :**

If

verify that (AB)^{T} = B^{T}A^{T }

**Question 4 :**

Prove that

are inverse to each other under matrix multiplication.

**Solution :**

If A is a square matrix of order n, and if there exists a square matrix B of the same order n, such that

AB = BA = I

where I is the unit matrix of order n, then B is called the multiplicative inverse matrix of A.

**Question 5 :**

If

find (A + B)C and AC + BC. Is (A + B)C = AC + BC ?

**Solution :**

L.H.S :

Add matrices A and B, then multiply (A + B) by C.

R.H.S :

Multiply the matrices A and C. Multiply the matrices B and C.

Add the matrices AC and BC.

So, (A + B)C and AC + BC are equal.

**Question 6 :**

If A and B are square matrices such that

AB = I and BA = I

then B is

(A) Unit matrix

(B) Null matrix

(C) Multiplicative inverse matrix of A

(D) -A

**Solution :**

If A is a square matrix of order n, and if there exists a square matrix B of the same order n, such that

AB = BA = I

Then,

Matrices A and B are inverse to each other.

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