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Inverse of a Matrix Video Lecture | Mathematics (Maths) for JEE Main & Advanced

FAQs on Inverse of a Matrix Video Lecture - Mathematics (Maths) for JEE Main & Advanced

1. What is the method to find the inverse of a matrix ?

Ans. To find the inverse of a matrix, you can use several methods, but the most common one is using the formula for the inverse of a 2x2 matrix or applying the Gauss-Jordan elimination method for larger matrices. For a 2x2 matrix A = [[a, b], [c, d]], the inverse A^-1 is given by (1/det(A)) * [[d, -b], [-c, a]], where det(A) = ad - bc. For larger matrices, you can augment the matrix with the identity matrix and perform row operations until the left side becomes the identity matrix.

2. Under what conditions does a matrix have an inverse ?

Ans. A matrix has an inverse if it is square (same number of rows and columns) and its determinant is non-zero. If the determinant is zero, the matrix is singular, and it does not have an inverse.

3. How can you check if the inverse of a matrix is correct ?

Ans. To check if the inverse of a matrix A is correct, you can multiply A by its inverse A^-1. If A * A^-1 = I, where I is the identity matrix, then A^-1 is indeed the correct inverse of A.

4. What is the significance of the inverse of a matrix in solving linear equations ?

Ans. The inverse of a matrix is significant in solving linear equations because it allows you to find the solution to a system of equations represented in matrix form. If Ax = b, where A is the matrix of coefficients, x is the vector of variables, and b is the constant vector, you can multiply both sides by A^-1 to isolate x: x = A^-1b.

5. Can non-square matrices have inverses ?

Ans. No, non-square matrices cannot have inverses. Only square matrices (matrices with the same number of rows and columns) can have an inverse if they meet the criteria of having a non-zero determinant. Non-square matrices may have left or right inverses under specific conditions, but they do not have a two-sided inverse.

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Oct 07, 2025 Last updated

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	Mathematics (Maths) for JEE Main & Advanced 177 videos\|617 docs\|160 tests

Mathematics (Maths) for JEE Main & Advanced

177 videos|617 docs|160 tests

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