Verified answer

Hola

B^2 X^t = 16 * I - A^t

16 * I

...16.....0.......0

....0.....16......0

....0......0......16

A^t =

...0.....4.....4.

..-2....3......0

...2...-2....12

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16 I - A^t =

...16.....-4.....-4

....2.....13......0

...-2......2......4

******************************

B = (-2) * I

B^2 = (-2)^2 * I^2

B^2 = 4 * I

La inversa de B^2 es

(B^2)^-1 = (4)^-1 * I^-1

(B^2)^-1 = (1/4) * I

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Tenemos la ecuación

B^2 X^t = 16 * I - A^t

Premultiplicamos por la inversa de B^2

(B^2)^-1 B^2 X^t = (B^2)^(-1) * (16 I - A^t)

Por propiedad de inversa y de matriz unidad

X^t = (B^2)^(-1) * (16 I - A^t)

remplazamos

X^t = (1/4) * I * (16 I - A^t)

Nos queda

X^t = (1/4) *

...16.....-4.....-4

....2.....13......0

...-2......2......4

X^t =

......4.....-1.......-1

....1/2..13/4......0

...-1/2...1/2......1

finalmente

X = (X^t)^t =

......4....1/2..-1/2

....-1..13/4....1/2

...-1......0.......1

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Verificado con Excel

Saludos