# NCERT Solutions for Class 12 Maths Determinants

Hi Students, Welcome to **Amans Maths Blogs (AMB)**. In this post, you will get the * NCERT Solutions for Class 12 Maths Determinants Exercise 4.5*. This

**can be downloaded in PDF file. The downloading link is given at last.**

*NCERT Solutions** NCERT Solutions for Class 12 Maths* are not only the solutions of Maths exercise but it builds your foundation of other important subjects. Getting knowledge of depth concept of

*like Algebra, Calculus, Trigonometry, Coordinate Geometry help you to understand the concept of Physics and Physical Chemistry.*

**CBSE Class 12**^{th}Maths* CBSE Class 12^{th}* is an important school class in your life as you take some serious decision about your career. And out of all subjects, Maths is an important and core subjects. So

*is major role in your exam preparation as it has detailed chapter wise solutions for all exercise.*

**CBSE NCERT Solutions for Class 12**^{th}MathsAs we know that all the schools affiliated from CBSE follow the NCERT books for all subjects. You can check the **CBSE NCERT Syllabus**. Thus, * NCERT Solutions* helps the students to solve the exercise questions as given in

*.*

**NCERT Books**## NCERT Solutions for Class 12 Maths Determinants Exercise 4.5

Find adjoint of each of the matrices in Exercises 1 and 2.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 1.**

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 2.**

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Verify A (adj A) = (adj A) A = |A| I in Exercises 3 and 4.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 3.**

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**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 4.**

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Find the inverse of each of the matrices (if it exists) given in Exercises 5 to 11.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 5.**

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**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 6.**

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**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 7.**

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**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 8.**

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**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 9.**

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**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 10.**

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**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 11.**

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**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 12.**

Let A = and B = . Verify that (AB)^{–1} = B^{–1}A^{–1}.

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**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 13.**

If A = , Show that A^{2} – 5A + 7I = O. Hence find A^{–1}.

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**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 14.**

For the matrix A = , find the numbers a and b such that A^{2} + aA + bI = O.

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**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 15.**

For the matrix A = , Show that A3– 6A2 + 5A + 11 I = O. Hence, find A^{–1}.

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**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 16.**

If A =, Verify that A^{3} – 6A^{2} + 9A – 4I = O and hence find A^{–1}.

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**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 17.**

Let A be a nonsingular square matrix of order 3 × 3. Then |adj A| is equal to

(A) |A|

(B) |A|^{2 }

(C) |A|^{3 }

(D) 3|A|

**NCERT Solutions:**

(B) For any n x n matrix A, det(adj A) = |adj A| = |A|^{n-1}. (It holds for singular and non-singular matrices.)

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.5: Ques No 18.**

If A is an invertible matrix of order 2, then det (A^{–1}) is equal to

(A) det (A)

(B) 1/det (A)

(C) 1

(D) 0

**NCERT Solutions:**

(B) If A is an invertible matrix of order 2, then AA^{-1} = I_{2} = A^{-1}A, where I2 is an identity matrix of order 2. So, det(AA-1) = det(I)

So, detA.detA^{-1} = 1,

Thus, detA^{-1} = 1/detA, where detA is non zero.