Which of the following statements about real matrices is correct?

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Which of the following statements about 2×22\times 2 real matrices is correct? (a) The product of two non-zero 2×22\times 2 matrices can never be the zero matrix. (b) There exist two non-zero 2×22\times 2 matrices whose product is the zero matrix. (c) If AB=OAB=O, then det⁡A=det⁡B=0\det A=\det B=0.},{ (d) If det⁡A=0\det A=0 and det⁡B=0\det B=0, then ABAB must be the zero matrix.

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