Using the properties of determinants, show that \(\left| \begin{matrix} 2 & 7 & 65 \\ 3 & 8 & 75 \\ 5 & 9 & 86 \end{matrix} \right| \) = 0

Using co-factors of elements of  second column evaluate \(\left| \begin{matrix} 6 & -1 & 5 \\ 3 & 0 & 4 \\ -2 & 7 & -3 \end{matrix} \right| \)

Find the adjoint of the matrix \(\left[ \begin{matrix} 2 & -1 & 3 \\ 0 & 5 & 1 \\ 3 & 6 & 8 \end{matrix} \right] \)

If A = \(\begin{bmatrix} 3 & 2 \\ 7 & 5 \end{bmatrix}\) and B = \(\begin{bmatrix} 4 & 6 \\ 3 & 2 \end{bmatrix}\), verify that (AB)^-1 = B^-1A^-1

Find the numbers a and b such that A² + aA + bI = 0 for the matrix A =\(\begin{bmatrix} 3 & 2 \\ 1 & 1 \end{bmatrix}\)