Maths Chapter 3 Matrices Notes PDF Class 12 for FREE Download
FAQs on Matrices Class 12 Notes: CBSE Maths Chapter 3
1. What is the core definition of a matrix and its order that I should remember for revision?
A matrix is a rectangular arrangement of numbers or functions, called elements, organized into rows and columns. The order of a matrix specifies its size, written as m × n, where 'm' is the number of rows and 'n' is the number of columns. This is a key term to remember for all matrix operations as per the CBSE 2025-26 syllabus.
2. How can I quickly summarise the main types of matrices for revision?
For a quick recap, focus on these key types of matrices:
- Row Matrix: Has only one row (order 1 × n).
- Column Matrix: Has only one column (order m × 1).
- Square Matrix: The number of rows equals the number of columns (order n × n).
- Diagonal Matrix: A square matrix where all non-diagonal elements are zero.
- Scalar Matrix: A diagonal matrix where all diagonal elements are the same non-zero constant.
- Identity Matrix (I): A special scalar matrix where all diagonal elements are 1.
- Zero Matrix (O): A matrix where all elements are zero.
3. What is the fundamental rule for adding or subtracting matrices?
The most important rule to remember is that two matrices can be added or subtracted only if they have the same order. The operation is then performed by adding or subtracting the corresponding elements of the two matrices to form a new matrix of the same order.
4. What is the process for multiplying a matrix by a scalar?
To perform scalar multiplication, you simply multiply every single element inside the matrix by the scalar (the constant number). The order of the resulting matrix remains the same as the original matrix. For example, if you multiply a matrix A by the scalar 3, every element in A gets multiplied by 3.
5. What conditions must be met for two matrices to be equal?
Two matrices, A and B, are considered equal if and only if two conditions are met:
- They must have the same order (same number of rows and columns).
- Each element of matrix A must be equal to the corresponding element of matrix B (i.e., aij = bij for all i and j).
6. What is the primary condition required to multiply two matrices?
To find the product of two matrices, say AB, the number of columns in the first matrix (A) must be equal to the number of rows in the second matrix (B). If this condition is not met, the matrices cannot be multiplied.
7. How do you quickly differentiate between a Symmetric and a Skew-Symmetric matrix?
Both are types of square matrices. The quick check involves their transpose (A'):
- A matrix A is Symmetric if it is equal to its transpose (A = A'). This means the elements aij = aji for all i and j.
- A matrix A is Skew-Symmetric if it is equal to the negative of its transpose (A = -A'). This implies its diagonal elements must all be zero, and aij = -aji.
8. What is the inverse of a matrix and when does it exist?
The inverse of a square matrix A, denoted as A-1, is another matrix such that when multiplied by A, it results in the identity matrix (I). So, AA-1 = A-1A = I. A key condition to remember is that a matrix's inverse exists only if the matrix is non-singular, which means its determinant is not zero (det(A) ≠ 0).
9. Why is matrix multiplication generally not commutative (AB ≠ BA)?
Matrix multiplication is not commutative for two main reasons. Firstly, the product BA may not even be defined if the number of columns in B doesn't match the number of rows in A, even if AB is defined. Secondly, even if both products are defined, the calculation process of multiplying rows by columns typically results in different elements for AB compared to BA. Commutativity is a special case, not the general rule.
10. What is the significance of the Identity Matrix in matrix operations?
The Identity Matrix (I) acts as the multiplicative identity in matrix algebra, much like the number '1' works in regular arithmetic. For any square matrix A, multiplying it by the identity matrix of the same order leaves the matrix unchanged (AI = IA = A). This property is fundamental for defining and verifying the inverse of a matrix.
11. Why must the columns of the first matrix match the rows of the second for multiplication to be possible?
This rule is essential because of how matrix multiplication is defined. Each element in the resulting matrix is calculated by performing a dot product of a row from the first matrix and a column from the second. For this to work, the number of elements in the row (which equals the number of columns in the first matrix) must exactly match the number of elements in the column (which equals the number of rows in the second matrix). Without this match, the element-wise multiplication and summation cannot be completed.
12. What is a good way to structure my revision for the Matrices chapter?
For an effective revision of Matrices for the 2025-26 CBSE exams, follow this structure:
- Start with the basic definitions: matrix, order, and the different types of matrices.
- Master the operations: addition, subtraction, scalar multiplication, and matrix multiplication, paying close attention to the conditions required for each.
- Understand the concept of the Transpose and its key properties.
- Connect the transpose to Symmetric and Skew-Symmetric matrices.
- Finally, cover the Inverse of a Matrix and the conditions for its existence. Practice solving problems involving all these concepts.

















