$A$ and $B$ are $3 \times 3$ matrices such that $AB + A + B = 0$,then:

Let $A$ and $B$ be two $3 \times 3$ real matrices such that $(A^{2}-B^{2})$ is an invertible matrix. If $A^{5}=B^{5}$ and $A^{3} B^{2}=A^{2} B^{3}$,then the value of the determinant of the matrix $A^{3}+B^{3}$ is equal to:

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

If $a, b, c, d, e, f$ are in $G.P.$,then the value of $\left| \begin{array}{ccc} a^2 & d^2 & x \\ b^2 & e^2 & y \\ c^2 & f^2 & z \end{array} \right|$ depends on

If $A_i = \begin{bmatrix} a^i & b^i \\ b^i & a^i \end{bmatrix}$ and if $|a| < 1, |b| < 1$,then $\sum_{i=1}^{\infty} \det(A_i)$ is equal to

If $A = \begin{bmatrix} -8 & 5 \\ 2 & 4 \end{bmatrix}$ satisfies the equation $x^2 + 4x - p = 0$, then $p$ is equal to