Question

If Aand Sare invertible nxnmatrices, then matrices Aand${\mathbf{S}}^{\mathbf{T}}\mathbf{AS}$must be similar.

Short answer

The given statement is FALSE.

Step-by-step solution

Check whether the given statement is TRUE or FALSE

Let A=l and S=2l.

Then,${\mathrm{S}}^{\mathrm{T}}\mathrm{AS}=4\mathrm{l}$which is not similar to a since the eigenvalues of ${\mathrm{S}}^{\mathrm{T}}\mathrm{AS}=4\mathrm{l}$and A = l are different.

Final Answer

The given statement is FALSE.