Matrix

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #121

Find the inverse of the following matrix by using Elementary column operations. $ \begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix} $

Question No: #122

For any square matrix `A`, wrong statement is -- (a) `(adj\ A)^{-1} = adj\ (A^{-1})`, (b) `(A^T)^{-1} = (A^{-1})^T`, (c) `(A^3)^{-1} = (A^{-1})^3`, (d) none of these.

Question No: #123

`A` and `B` are two matrices such that `AB = BA`. Then show that `A^2+B^2 = A+B`

Question No: #124

Prove that any square matrix can be expressed as the sum of a symmetric matrix and a skew-symmetric matrix.

Question No: #125

If `A` is a square matrix, then show that the matrices `A\cdotA^T` and `A^T\cdotA` are symmetric.

Question No: #126

If `A` and `B` are two symmetric matrices of same order, then show that `(AB-BA)` is a skew-symmetric matrix.

Question No: #127

If `A` is a skew symmetric matrix, then show that `A^2` is a symmetric matrix.

Question No: #128

If `A` is a skew-symmetric matrix and `I+A` isa non-singular matrix, then show that `(I-A)(I+A)^{-1}` is an orthogonal matrix.

Question No: #129

If `A` and `B` are two square matrices of same order and `A^{-1}`, `B^{-1}` exist. Then prove that inverse of `AB` also exists and `(AB)^{-1} = B^{-1]A^{-1}`.

Question No: #130

Prove that inverse of any square matrix (if exists) is unique.