For what value of x will |\( 8{ A }^{ T } \)| =0 if A = \(\begin{bmatrix}2 & 1\\x^2 & 8 \end{bmatrix}\)?

Both (a) and (b)

Given that |8\( { A }^{ T } \)| =0

Also, |\(8 { A }^{ T } \)| = \( { 8 }^{ 2 } \) |\( { A }^{ T } \)|

                                      = \( { 8 }^{ 2 } \) |A |

                                      = 64|A|

Because |\( { A }^{ T } \) = |A |

So, 0 =64 |A|

|A| = 0

\( { x }^{ 2 } \)-16 = 0

\( { x }^{ 2 } \) = 16

x= 4 and -4