Question
Asked Nov 12, 2019
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please answer only part (c)

a11
a12
is the matrix:
a22,
(4) The adjugate of a 2 x 2 matrix A
a21
a12
a22
adj(A)
a11
-a21
A adj (A) det(A)I2.
(a) Show that adj(A) A
det(A)
(b) Show that det(adj(A))
(c) Show that if A is invertible, then A-1= [det(A)]ladj(A)
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a11 a12 is the matrix: a22, (4) The adjugate of a 2 x 2 matrix A a21 a12 a22 adj(A) a11 -a21 A adj (A) det(A)I2. (a) Show that adj(A) A det(A) (b) Show that det(adj(A)) (c) Show that if A is invertible, then A-1= [det(A)]ladj(A)

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Expert Answer

Step 1

Step 2

...
Ar A-ad (A) A det (A)I
I adj (A)-A det(4) (^A-1
adj (A) Adet (A)1,
adj (A)
det(A
Adet (A)ad (A)
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Ar A-ad (A) A det (A)I I adj (A)-A det(4) (^A-1 adj (A) Adet (A)1, adj (A) det(A Adet (A)ad (A)

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