If $A=\left[\begin{array}{ll}0 & 3 \\ 0 & 0\end{array}\right]$ and $f(x)=x+x^2+x^3+\ldots \ldots+x^{2023}$, then $f(A)+I=$

4. If $A=\left[\begin{array}{lll}b & a & 0 \\ c & 0 & b \\ a & a & b\end{array}\right]$ and $B=\left[\begin{array}{lll}0 & a & b \\ b & 0 & c \\ b & a & a\end{array}\right]$ are two matrices such that $A B=\left[\begin{array}{ccc}2 & 2 & 7 \\ 1 & 8 & 5 \\ 3 & 6 & 10\end{array}\right]$, then $a^2+b^2+c^2=$

If $A=\left[\begin{array}{lll}1 & a & 3 \\ b & 2 & c \\ 3 & d & 4\end{array}\right]$ is a symmetric matrix and $B=\left[\begin{array}{ccc}0 & 5 & b \\ -5 & 0 & -7 \\ 6 & c & 0\end{array}\right]$ is a skew-symmetric matrix, then $A B=$

If the inverse of the matrix $A=\left[\begin{array}{ccc}-1 & -3 & -2 \\ 0 & 1 & 2 \\ 3 & 4 & 5\end{array}\right]$ is $A^{-1}=\left[\begin{array}{lll}a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3\end{array}\right]$, then $a_1+c_2+b_3=$