$f命题：$$f(12浙大一)$设$E$为$n$阶单位阵，$M = left( {egin{array}{*{20}{c}}0&E \ { - E}&0 end{array}} ight),{A^T}MA = M$，证明：$left| A ight| = 1$
1
$f命题：$设$A = {A_{n imes n}},alpha ,eta in {F^n}$，证明：$left| {egin{array}{*{20}{c}}A&eta \ {{alpha ^T}}&k end{array}} ight| = left| A ight|k - {alpha ^T}{A^*}eta $
1
$f命题：$