Matrices And Determinants

Fill in all the gaps, then press "Check" to check your answers. Use the "Hint" button to get a free letter if an answer is giving you trouble. You can also click on the "[?]" button to get a clue. Note that you will lose points if you ask for hints or clues!

Write true or false in the given blanks: (Q1 - Q7)
1. Every invertible matrix possesses a unique inverse.
2. A square matrix is invertible iff it is singular.
3. If A is a non-singular matrix, then

A^{- 1} = \frac{1}{|\begin{matrix} A \end{matrix}|}

.
4. If A is an invertible matrix, then

{(A^{- 1})}^{- 1} = A

.
5. If A and B are two invertible matrices of the same order, then

(A B^{- 1}) = A^{- 1} B^{- 1}

.
6. If A is an invertible matrix, then

{(A^{T})}^{- 1} = {(A^{- 1})}^{T}

.
7. The inverse of an invertible symmetric matrix is a symmetric matrix.
8. A matrix obtained from and identity matrix by a single elementary operation is called matrix.
9. The transpose of the matrix of cofactors of elements of A is called the of A.
10. Given

[\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 5 \end{matrix}]

is an example of matrix.

Matrices And Determinants

Gap-fill exercise