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Identity Matrix Video Lecture | Mathematics (Maths) Class 12 - JEE
FAQs on Identity Matrix Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. What is an identity matrix? |  |
Ans. An identity matrix is a square matrix in which all the elements in the main diagonal are ones, while all the other elements are zeros. It is denoted by the symbol "I" or "I_n", where "n" represents the size of the matrix.
| 2. What are the properties of an identity matrix? | |
Ans. The properties of an identity matrix include:
- The product of any matrix and its corresponding identity matrix is equal to the original matrix.
- The product of an identity matrix and any matrix is equal to the original matrix.
- The identity matrix is commutative under matrix multiplication.
| 3. How can we determine whether a matrix is an identity matrix or not? | |
Ans. To determine whether a matrix is an identity matrix, we need to check the following conditions:
- The matrix must be square, i.e., it should have an equal number of rows and columns.
- All the elements in the main diagonal should be ones.
- All the elements outside the main diagonal should be zeros.
| 4. What is the significance of an identity matrix in matrix operations? | |
Ans. The identity matrix serves as the equivalent of the number "1" in matrix operations. When a matrix is multiplied by the identity matrix, it remains unchanged. It acts as a neutral element, similar to how multiplying a number by 1 does not change its value. The identity matrix plays a crucial role in solving systems of linear equations, matrix inverses, and other matrix operations.
| 5. Can an identity matrix have a size other than a square matrix? | |
Ans. No, an identity matrix is always a square matrix. This means that it has an equal number of rows and columns. Each square matrix has a unique identity matrix associated with it, and its size is determined by the number of rows (or columns) it has.
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