If A and B are square matrices of same order such that, $AB=BA$, $A^{-1} = A^2$ and $B^{-1} = B^3$, then the value of $(AB)^{2040}$, is

If $A=\begin{bmatrix}1 & 2 & 2\\2 & 1 & -2\\\alpha & 2 & \beta\end{bmatrix}$ and $AA^T=9I$, where I is the identity matrix of order 3, then $(\beta-\alpha)$ equals:

If $P$, $Q$ and $R$ are three singular matrices given by $P = \begin{bmatrix} 2 & 3a \\ 4 & 3 \end{bmatrix}$, $Q = \begin{bmatrix} b & 5 \\ 2a & 6 \end{bmatrix}$ and $R = \begin{bmatrix} a^2 + b^2 - c & 1 - c \\ c + 1 & c \end{bmatrix}$, then the value of $(2a + 6b + 17c)$ is

The sum of a matrix $A$ and its transpose is $\begin{bmatrix}6 & -1\\ -1 & 4\end{bmatrix}$.

Which of the following statements is true?

If the matrix $\begin{bmatrix}3 & 2a & -5\\4 & 0 & b\\-5 & 3 & 10\end{bmatrix}$ is symmetric, then the value of $5a + 2b$ is

If A is a skew-symmetric matrix then, the matrix $B^TAB$ is:-

If matrix A is of order $2 \times 3$ and B of order $3 \times 2$, then