Can we obtain a diagonal matrix by multiplying two non-diagonal matrices? give an example

Yes, we can obtain a diagonal matrix by multiplying two non diagonal matrix.

Consider the matrix multiplication below



For the product to be a diagonal matrix,

a f + b h = 0 ⇒ a f = -b h
and c e + d g = 0 ⇒ c e = -d g

Consider the following sets of values



The the matrix product becomes:



Thus, as can be seen we can obtain a diagonal matrix that is a product of non diagonal matrices.

Yes, we can obtain a diagonal matrix by multiplying two non-diagonal matrices. A diagonal matrix is a matrix where all the elements beyond the diagonal are zeros. This is an example.

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