List of top Mathematics Questions on Invertible Matrices

If A is a non-identity invertible symmetric matrix, then \(A^{-1}\) is:

Which of the following matrices can NOT be obtained from the matrix \(\begin{bmatrix} -1 &2 \\  1 & -1 \end{bmatrix}\) by a single elementary row operation?

The number of matrices of order 3 × 3, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is _________.

If A and B are invertible matrices then which of the following is not correct ?

The inverse of the matrix $\begin{bmatrix}2&5&0\\ 0&1&1\\ -1&0&3\end{bmatrix} $ is

If matrix
\[ A = \begin{bmatrix} 3 & -2 & 4 \\ 1 & 2 & -1 \\ 0 & 1 & 1 \end{bmatrix}, \quad \text{and} \quad A^{-1} = \frac{1}{k} \, \text{adj}(A), \]
then \(k\) is:

If $A = \begin{bmatrix}2&-2\\ -2&2\end{bmatrix}$ then $A^n = 2^k A,$ where k =

If $A$ is a square matrix of order 3 , then | adj $\left(\operatorname{adj} A^{2}\right) \mid$ is equal to

If $A = \begin{bmatrix}1&1\\ 1&1\end{bmatrix}$ then $A^{100}$ :

If $a.b = a.c$ and $a \times b = a \times c$, then correct statement is

The number of $3 \times 3$ non-singular matrices with four entries as $1$ and all other entries as $0$ is

Let A=$\begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 &t \\ 4&7-t&-6 \\ \end{bmatrix}$, then the values of t for which inverse of A does not exist

The inverse of the matrix $\begin{bmatrix} {5}&{-2}\\ {3}&{1}\\ \end{bmatrix}$ is is

Two matrices A and B are multiplicative inverse of each other only if

The inverse of a symmetric matrix is :