Question

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

Answer 1

Verified

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