If $A$ is a square matrix such that $A^{2} = A$,then $(I + A)^{3} - 7A$ is equal to

Let $A$ and $B$ be two symmetric matrices of order $3$.
Statement $-1$: $A(BA)$ and $(AB)A$ are symmetric matrices.
Statement $-2$: $AB$ is a symmetric matrix if the matrix multiplication of $A$ with $B$ is commutative.

Let $X = \left\{\begin{bmatrix} a & b \\ c & d \end{bmatrix} : a, b, c, d \in \mathbb{R} \right\}$. Define $f: X \rightarrow \mathbb{R}$ by $f(A) = \operatorname{det}(A), \forall A \in X$. Then,$f$ is

If $C$ and $D$ are two $n \times n$ non-singular matrices over the set of real numbers $\mathbb{R}$ such that $CD = -DC$,then $n$ is:

Let $A$ be a $3 \times 3$ invertible matrix. If $|\operatorname{adj}(24A)| = |\operatorname{adj}(3 \operatorname{adj}(2A))|$,then $|A^2|$ is equal to

If $A$ and $B$ are square matrices of order $3$,then $|(A-A^T)+(B-B^T)|=$