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Andrej [43]
3 years ago
10

If D is an n × n diagonal matrix with entries dii, then det D = d11d22 ∙ ∙ ∙ dnn. Verify this theorem for 2 × 2 matrices.

Mathematics
1 answer:
nadya68 [22]3 years ago
8 0

Answer:

Verified

Step-by-step explanation:

Let the diagonal matrix D with size 2x2 be in the form of

\left[\begin{array}{cc}a&0\\0&d\end{array}\right]

Then the determinant of matrix D would be

det(D) = a*d - 0*0 = ad

This is the product of the matrix's diagonal numbers

So the theorem is true for 2x2 matrices

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