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Chapter 3: Matrices

NCERT Solutions for CBSE Class 10 Mathematics — 14 solved questions with detailed explanations.

14

Questions

0

Topics

Solved Questions

Q1. If A is a 3×2 matrix and B is a 2×4 matrix, then the order of AB is:

3×4
2×2
4×3
3×3

Difficulty: Easy · Topic: Matrix Multiplication

Solution

(3×2)(2×4) = 3×4. Number of columns of A must equal rows of B.

Q2. The trace of a 3×3 identity matrix is:

Difficulty: Easy · Topic: Trace

Solution

Trace = sum of diagonal elements = 1+1+1 = 3.

Q3. Trace of 2x2 identity matrix:

Difficulty: Easy · Topic: Matrix

Solution

Trace = sum of diagonal = 2.

Q4. Trace of 3x3 identity matrix:

Difficulty: Easy · Topic: Matrix

Solution

Trace = sum of diagonal = 3.

Q5. Trace of 4x4 identity matrix:

Difficulty: Easy · Topic: Matrix

Solution

Trace = sum of diagonal = 4.

Q6. Trace of 5x5 identity matrix:

Difficulty: Easy · Topic: Matrix

Solution

Trace = sum of diagonal = 5.

Q7. A square matrix A is orthogonal if:

A² = I
AAᵀ = I
A = Aᵀ
A + Aᵀ = 0

Difficulty: Easy-Medium · Topic: Orthogonal Matrix

Solution

Orthogonal matrix: AAᵀ = AᵀA = I, i.e., A⁻¹ = Aᵀ.

Q8. A+B = B+A shows matrix addition is:

distributive
associative
commutative
not defined

Difficulty: Easy-Medium · Topic: Matrix Properties

Solution

commutative.

Q9. AB ≠ BA in general shows multiplication is:

not commutative
distributive
commutative
associative

Difficulty: Easy-Medium · Topic: Matrix Properties

Solution

not commutative.

Q10. A square matrix with all diagonal elements 1 and rest 0 is:

symmetric matrix
null matrix
identity matrix
scalar matrix

Difficulty: Easy-Medium · Topic: Matrix Properties

Solution

identity matrix.

Q11. A matrix equal to its transpose is:

identity
orthogonal
symmetric
skew-symmetric

Difficulty: Easy-Medium · Topic: Matrix Properties

Solution

symmetric.

Q12. A matrix equal to negative of its transpose is:

null
orthogonal
symmetric
skew-symmetric

Difficulty: Easy-Medium · Topic: Matrix Properties

Solution

skew-symmetric.

Q13. (AB)' =:

A'B'
B'A'
(A'B')
AB

Difficulty: Easy-Medium · Topic: Matrix Properties

Solution

B'A'.

Q14. (AB)⁻¹ =:

A⁻¹B⁻¹
B⁻¹A⁻¹
BA
(AB)

Difficulty: Easy-Medium · Topic: Matrix Properties

Solution

B⁻¹A⁻¹.

Other Chapters in Mathematics

Ch 1: Relations & Functions Ch 2: Inverse Trig Functions Ch 4: Determinants Ch 5: Continuity & Differentiability Ch 6: Applications of Derivatives Ch 7: Integrals Ch 8: Applications of Integrals Ch 9: Differential Equations Ch 10: Vector Algebra Ch 11: Three Dimensional Geometry Ch 12: Linear Programming Ch 13: Probability

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