Question

Write value of $\textstyle\int$ sec x(sec x + tan x) dx

If A is a square matrix and | A | = 2, then write the value of | AA’ |, where A’ is the transpose of matrix A.

Find matrix A such that. $\left(\begin{array}{l l}{2}&{-1}\\ {1}&{0}\\ {-3}&{4}\end{array}\right)$ $A={\left(\begin{array}{l l}{-1}&{-8}\\ {1}&{-2}\\ {9}&{22}\end{array}\right)}$

Write the value of x - y + z from following equation. $\left(\begin{array}{l }x+y+z \\ x+z \\ y+z\end{array}\right)$ = $\left(\begin{array}{l }9 \\ 5 \\ 7\end{array}\right)$

If matrix A = $\left(\begin{array}{l l }2 & -2 \\ -2 & 2\end{array}\right)$ and A² = pA, then write the value of p.

Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.

If A and B are invertible matrices of order 3, $|\mathbf{A}|=$ 2 and $|(\mathbf{AB})^{-1}|\,=\,-{\frac{1}{6}}.$ Find $|\mathbf{B}$.