Question 1: Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = IA

Question 2: Find the inverse of each of the matrices, if it exists.

 Answer

We know that A=IA

Question 3: Find the inverse of each of the matrices, if it exists.

Answer

We know that A=IA

Question 4: Find the inverse of each of the matrices, if it exists.

Answer

We know that A = IA

Question 5: Find the inverse of each of the matrices, if it exists.

Answer

We know that A = IA

Question 6: Find the inverse of each of the matrices, if it exists.

Answer

We know that A = IA

Question 7: Find the inverse of each of the matrices, if it exists.

Answer

We know that A = AI

Question 8: Find the inverse of each of the matrices, if it exists.

Answer

We know that A = IA

Question 9: Find the inverse of each of the matrices, if it exists.

Answer

We know that A = IA

 

Question 10: Find the inverse of each of the matrices, if it exists.

Answer

We know that A = AI

Question 11: Find the inverse of each of the matrices, if it exists.

Answer

We know that A = AI

Question 12: Find the inverse of each of the matrices, if it exists.

Answer

We know that A = IA

Now, in the above equation, we can see all the zeros in the second row of the matrix on the L.H.S.

Therefore, A ⁻¹ does not exist.

Question 13: Find the inverse of each of the matrices, if it exists.

Answer

We know that A = IA

Question 14: Find the inverse of each of the matrices, if it exists.

Answer

We know that A = IA

Applying R₁ → R₁ – ½ R_2,  we have:

Now, in the above equation, we can see all the zeros in the first row of the matrix on the L.H.S.

Therefore, A −1 does not exist.

 

Question 16: Find the inverse of each of the matrices, if it exists.

Answer

We know that A = IA

Applying R₂ → R₂ + 3R₁ and R₃ → R₃ − 2R₁, we have:

Applying R₁ → R₁ + 3R₃ and R₂ → R₂ − 8R₃, we have:

Applying R₃ → R₃ + R₂, we have:

Applying R₃ → 1/25 R₃, we have:

Applying R₁ → R₁ - 10R₃ and R₂ → R₂ − 21R₃, we have:

Question 17: Find the inverse of each of the matrices, if it exists.

Answer

We know that A = IA

Applying R₁→ ½ R₁, we have:

 Applying R₂→ R₂-5R₁, we have:

Applying R₃→ R₃-R₂, we have:

Applying R₃→ 2R₃, we have:

Applying R₁→ R₁+ ½ R₃, and R₂→ R₂+ 5/2  R3,we have:

Question 18: Matrices A and B will be inverse of each other only if

A. AB = BA                                       B. AB = BA = 0

C. AB = 0, BA = I                             D. AB = BA = I

Answer

Answer: D We know that if A is a square matrix of order m, and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is said to be the inverse of A. In this case, it is clear that A is the inverse of B.

Thus, matrices A and B will be inverses of each other only if AB = BA = I