ECET 2026 CSE – Matrices: Types & Operations (Day 1 – Morning Session)

🔰 Introduction

Welcome to Day 1 – Morning Session of your ECET 2026 CSE Mathematics preparation! In this session, we dive into Matrices – Types & Operations, a topic crucial for mastering engineering mathematics. Aligned with the C-23 curriculum, this concept not only strengthens your fundamentals but also boosts your speed in solving ECET questions, especially when matrix problems appear in linear equations, transformations, and computer applications. Let’s get started with clear notes, practice questions, and expert explanations!

📘 Concept Notes: Matrices – Types & Operations

🔹 What is a Matrix?

A matrix is a rectangular array of numbers or functions arranged in rows and columns. It’s a powerful tool used in solving systems of linear equations, computer graphics, and network theory.

🔹 Types of Matrices:

1. Row Matrix: Only one row (e.g., 1×n)
2. Column Matrix: Only one column (e.g., n×1)
3. Square Matrix: Same number of rows and columns (e.g., 3×3)
4. Zero Matrix: All elements are 0
5. Diagonal Matrix: All non-diagonal elements are zero
6. Scalar Matrix: A diagonal matrix with equal diagonal elements
7. Identity Matrix (I): A diagonal matrix with all diagonal elements = 1
8. Symmetric Matrix: A = Aᵗ (transpose is same)
9. Skew-Symmetric Matrix: Aᵗ = –A

🔹 Matrix Operations:

1. Addition/Subtraction: Same dimensions required
2. Scalar Multiplication: Multiply all elements by a scalar
3. Matrix Multiplication: If A is m×n and B is n×p, result is m×p
4. Transpose (Aᵗ): Rows become columns
5. Determinant: Defined only for square matrices
6. Inverse: If A⁻¹ exists, then A×A⁻¹ = I

🧠 Tip: In ECET, matrix multiplication and inverse are hot topics. Practice makes perfect!

🔟 10 Most Expected ECET 2026 MCQs – Matrices

Q1. Which of the following is a square matrix?
A) [1 2 3]
B) [4; 5; 6]
C) [[1 2]; [3 4]]
D) [[7 8 9 0]]

Q2. If A is a 2×3 matrix and B is a 3×4 matrix, what is the order of AB?
A) 2×3
B) 3×3
C) 2×4
D) 4×3

Q3. The identity matrix of order 3 is:
A) [[0 0 0]; [0 0 0]; [0 0 0]]
B) [[1 0 0]; [0 1 0]; [0 0 1]]
C) [[1 1 1]; [1 1 1]; [1 1 1]]
D) [[0 1 0]; [1 0 1]; [0 1 0]]

Q4. What is the transpose of [[1 2]; [3 4]]?
A) [[1 3]; [2 4]]
B) [[1 2]; [4 3]]
C) [[4 3]; [2 1]]
D) [[1 4]; [2 3]]

Q5. Which condition is required for matrix multiplication A×B to be valid?
A) Columns of A = Rows of B
B) Rows of A = Rows of B
C) Columns of A = Columns of B
D) None of the above

Q6. If A = [[2 0]; [0 2]], then A is a:
A) Diagonal matrix
B) Scalar matrix
C) Both A and B
D) Identity matrix

Q7. A matrix A is symmetric if:
A) A = A⁻¹
B) A = –Aᵗ
C) A = Aᵗ
D) A = 0

Q8. The determinant of [[1 2]; [3 4]] is:
A) –2
B) 10
C) –5
D) 2

Q9. The inverse of identity matrix I is:
A) I
B) 0
C) Not defined
D) I⁻²

Q10. If A is a skew-symmetric matrix, then the diagonal elements of A are:
A) 1
B) 0
C) –1
D) Any number

✅ Answer Key Table

Q.No	Answer
Q1	C
Q2	C
Q3	B
Q4	A
Q5	A
Q6	C
Q7	C
Q8	C
Q9	A
Q10	B

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🧠 Answer Explanations

Q1: A square matrix has equal rows and columns. Option C is 2×2.

Q2: Matrix multiplication is valid if A’s columns = B’s rows. A(2×3), B(3×4) → Result is 2×4.

Q3: Identity matrix has 1’s on the diagonal and 0’s elsewhere. Option B fits.

Q4: Transpose flips rows to columns: [[1 2]; [3 4]] → [[1 3]; [2 4]].

Q5: For A×B, A’s columns = B’s rows.

Q6: A diagonal matrix where all diagonal elements are same is also scalar. So, both A and B.

Q7: Symmetric matrix means A = Aᵗ.

Q8: Determinant = (1×4) – (2×3) = 4 – 6 = –2.

Q9: Inverse of identity matrix is itself: I⁻¹ = I.

Q10: Skew-symmetric matrices have 0 on diagonals.

🎯 Why This Practice Matters

Practicing matrix-based MCQs boosts your speed, accuracy, and confidence in ECET 2026. These concepts directly appear in multiple ECET questions, especially in the Mathematics section (50 marks). With regular revision, you’ll find these questions to be easy scoring!

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