For $I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, if $X$ and $Y$ are square matrices of order $2$ such that $X Y=X$ and $Y X=Y$, then $\left(\mathrm{Y}^{2}+2 \mathrm{Y}\right)$ equals to :

Match the LIST-I with LIST-II

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If $A$ is a skew-symmetric matrix of order 5, then $|adjA|$ is equal to

Which of the following statements is (are) true?

(A) $B^T AB$ is a skew-symmetric matrix if A is a symmetric matrix

(B) $B^T AB$ is a symmetric matrix if A is a symmetric matrix

(C) $B^T AB$ is a symmetric matrix if A is a skew-symmetric matrix

(D) $B^T AB$ is a skew-symmetric matrix if B is a skew-symmetric matrix

(E) $B^T AB$ is a symmetric matrix if B is a symmetric matrix

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If $A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 2 & 3 & -1 \end{bmatrix}$, then $A^2$ is equal to

$A = \begin{bmatrix} 1/3 & 2 \\ 0 & 2x - 3 \end{bmatrix}$ & $B = \begin{bmatrix} 3 & 6 \\ 0 & -1 \end{bmatrix}$ If $AB = I$ (Where I is an identity matrix of order 2) , then value of x is

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