Matrices: A Complete Guide for Class 12 (WB HS Exam)
Matrices: A Complete Guide for Class 12 WB HS Exam (Concepts + MCQs)
.png)
๐น Introduction to Matrices
A matrix is a rectangular array of numbers arranged in rows and columns. It is a fundamental part of Class 12 Mathematics and is widely used in solving linear equations, transformations, and determinants.
For West Bengal Higher Secondary (WB HS) Mathematics, matrices are crucial because they help in solving system of equations, calculus, and transformations, making them one of the most scoring topics in your syllabus.
Scroll down for MCQs ↓ ↓ ↓
๐น Types of Matrices (Important for WB HS Exam)
1️⃣ Row Matrix – A matrix with only one row.
2️⃣ Column Matrix – A matrix with only one column.
3️⃣ Square Matrix – A matrix with equal rows and columns.
4️⃣ Diagonal Matrix – A square matrix where non-diagonal elements are zero.
5️⃣ Identity Matrix (I) – A diagonal matrix with 1s on the diagonal.
6️⃣ Zero Matrix – A matrix where all elements are zero.
Scroll down for MCQs ↓ ↓ ↓
๐น Matrix Operations (Key Formulas & Rules)
✅ Addition & Subtraction – Possible only if matrices have the same order.
✅ Multiplication Rule – Order matters (AB ≠ BA in most cases).
✅ Transpose of a Matrix (Aแต) – Switching rows and columns.
✅ Determinant of a Matrix (|A|) – A key scalar value used in equations.
✅ Inverse of a Matrix (A⁻¹) – Exists only if |A| ≠ 0.
๐ Tip: The inverse matrix formula is:
๐น Most Important MCQs for WB HS Exam
๐ Basic Matrix Concepts
1️⃣ A matrix is a:
✅ b) Rectangular array of numbers
2️⃣ The order of a 2 × 3 matrix is:
✅ b) 2 × 3
3️⃣ A square matrix has:
✅ a) Equal number of rows and columns
๐ Matrix Operations & Properties
4️⃣ If A + B is defined, then matrices A and B must have:
✅ a) The same order
5️⃣ If A = [1 2; 3 4], then A² is:
✅ a) [7 10; 15 22]
6️⃣ The determinant |A| is defined for:
✅ a) Square matrices
๐ Determinants & Inverses
7️⃣ If A is a singular matrix, then |A| is:
✅ a) 0
8️⃣ If A is invertible, then A⁻¹ satisfies:
✅ a) AA⁻¹ = I
9️⃣ If A and B are square matrices, then |AB| is:
✅ b) |A| × |B|
๐น More Important MCQs for WB HS Exam
๐ Matrix Properties & Special Matrices
๐ The trace of a square matrix is the sum of its:
✅ a) Diagonal elements
1️⃣1️⃣ A matrix with zero determinant is called:
✅ a) Singular
1️⃣2️⃣ The inverse of a matrix exists if and only if:
✅ a) |A| ≠ 0
1️⃣3️⃣ The identity matrix (I) satisfies:
✅ c) IA = AI = A
1️⃣4️⃣ If A is a diagonal matrix, then A² is:
✅ c) A diagonal matrix
1️⃣5️⃣ The determinant of a 2×2 matrix [a b; c d] is:
✅ a) |A| = ad - bc
1️⃣6️⃣ The determinant of a zero matrix is:
✅ b) 0
1️⃣7️⃣ The rank of a zero matrix is:
✅ c) 0
1️⃣8️⃣ If A is symmetric, then:
✅ b) Aแต = A
1️⃣9️⃣ If A is skew-symmetric, then:
✅ c) Aแต = -A
2️⃣0️⃣ The determinant of an identity matrix (Iโ) is always:
✅ a) 1
๐ Inverse, Adjoint & Transformations
2️⃣1️⃣ The inverse of an identity matrix is:
✅ a) The identity matrix itself
2️⃣2️⃣ The inverse of a diagonal matrix exists if:
✅ a) None of the diagonal elements are zero
2️⃣3️⃣ If A and B are invertible matrices, then the inverse of AB is:
✅ b) B⁻¹ A⁻¹
2️⃣4️⃣ The inverse of a triangular matrix is:
✅ b) Also a triangular matrix
2️⃣5️⃣ If A is an orthogonal matrix, then:
✅ c) Aแต = A⁻¹
2️⃣6️⃣ The sum of the diagonal elements of a square matrix is called:
✅ a) The trace of the matrix
2️⃣7️⃣ The determinant of an upper triangular matrix is:
✅ c) The product of its diagonal elements
๐ Advanced Matrix Concepts
2️⃣8️⃣ If A is a singular matrix, then A⁻¹:
✅ b) Does not exist
2️⃣9️⃣ If A² = A, then A is called:
✅ b) An idempotent matrix
3️⃣0️⃣ The determinant of a permutation matrix is:
✅ a) Either +1 or -1
3️⃣1️⃣ If two rows of a determinant are identical, then |A| is:
✅ b) 0
3️⃣2️⃣ A row transformation does not change the determinant of a matrix:
✅ a) True
3️⃣3️⃣ If AB = I, then B is:
✅ c) The inverse of A (A⁻¹)
๐น FAQs on Matrices (Class 12 WB HS Exam)
❓ What is the easiest way to solve matrix problems?
✔️ Focus on basic matrix operations, determinants, and inverse formulas.
❓ How do I remember determinant rules?
✔️ Use the Sarrus Rule for 3×3 matrices and Laplace Expansion for larger matrices.
❓ How many marks are matrices worth in the WB HS Exam?
✔️ Matrices & Determinants carry 8-10 marks in the West Bengal Higher Secondary Math Exam.
❓ What is the most important formula for matrices?
✔️ The Inverse Matrix Formula:
๐น Conclusion
Matrices play a key role in Class 12 WB HS Mathematics. By practicing matrix operations, determinants, and inverse calculations, you can easily score in your Higher Secondary Exam.
๐ก Want More Exam-Ready Content?
๐ Stay updated with important MCQs, study tips, and math tricks at MightyKnowledge! ๐
.png)
.png)