Evaluate: \(\begin{bmatrix} 3&-2&4\\2&0&1\\1&2&3 \end{bmatrix}\)

Find |AB| if \(A=\begin{bmatrix} 3&-1\\2&1 \end{bmatrix} \) and \(B =\begin{bmatrix} 3&0\\1&-2 \end{bmatrix}\)

Solve: \(\begin{vmatrix} x & 2 & -1 \\ 2 & 5 & x \\ -1 & 2 & x \end{vmatrix}=0.\)

Without actual expansion show that the value of the determinant \(\begin{vmatrix}5 &5^2 &5^3 \\5^2 & 5^3 & 5^4\\5^4&5^5&5^6 \end{vmatrix}\)is zero.

If A \(= \begin{bmatrix} 1 & -1 \\2 & 3 \end{bmatrix}\) show that A² - 4A + 5I₂ = 0 and also find A^-1.