(a)
We know that
det(A . B) = det(A) . det(B)
and A. A-1 = I
where I is the unit matrix.
For a unit matrix I, det(I) = 1
So, det(A. A-1 ) = det(I)
=> det(A) . det(A-1) = 1
=> det(A) = 1 / det(A-1)
(b)
We know that det(A . B) = det(A) . det(B)
Let A = B, then det(A . A) = det(A) . det(A)
Now,
det(A2) = det(A . A) = det(A) . det(A) = [det(A)]2
Thus, det(A2) = [det(A)]2
Please show work
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