Let be the set of all matrices with real entries. Define Det: byDet ca bc dd = ad bc.(a) Prove that Det: is operation preserving, wheredenotes with matrix multiplication.(b) Prove that Det: is not operation preserving, wheredenotes with matrix addition.

L22 - 9 ex. The radius of a sphere is determined using an instrument with a possible error in measurement of at most 0.03in. If the instrument ﬁnds the radius of a sphere to be 12 inches, what is the maximum error that can occur in using that measurement to ﬁnd the volume of the sphere ∆V Relative error: ≈ V Percentage error: