If-A-is-a-3-3-matrix-where-det-A-2-then-what-will-be-det-3A-2-A-1-knowing-that-A-1-is-the-inverse-of-A-

Question Number 149116 by bramlexs22 last updated on 03/Aug/21

If A is a 3 \times 3 matrix where \det (A) = - 2

then what will be \det ({3 A}^{2} A^{- 1}) ?

knowing that A^{- 1} is the inverse

of A

Answered by EDWIN88 last updated on 03/Aug/21

d e t (3 A^{2} A^{- 1}) = d e t (3 A) = 3^{3} \times d e t (A)

= 27 \times (- 2) = - 54

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