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Find A = [[1,2],[3,4]], B = [[2,-1],[-1,2]], (A * B)' = B' * A'

Solution:
Your problem -> A = [[1,2],[3,4]], B = [[2,-1],[-1,2]], (A * B)' = B' * A'

To find LHS = (A × B)^T

A×B=
 1 2 3 4
×
 2 -1 -1 2

=
 1×2+2×-1 1×-1+2×2 3×2+4×-1 3×-1+4×2

=
 2-2 -1+4 6-4 -3+8

=
 0 3 2 5

(A × B)^T =
 0 3 2 5
T
=
 0 2 3 5

:.(A × B)^T =
 0 2 3 5
 ->(1)

To find RHS = (B^T) × (A^T)

B^T =
 2 -1 -1 2
T
=
 2 -1 -1 2

A^T =
 1 2 3 4
T
=
 1 3 2 4

(B^T)×(A^T)=
 2 -1 -1 2
×
 1 3 2 4

=
 2×1-1×2 2×3-1×4 -1×1+2×2 -1×3+2×4

=
 2-2 6-4 -1+4 -3+8

=
 0 2 3 5

:.(B^T) × (A^T) =
 0 2 3 5
 ->(2)

From (1) and (2)
:. (A × B)^T=(B^T) × (A^T) (proved)

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