If , then show that .


Expanding along the first row



= 1(1×4 – 2×0) – 0(0×4 – 0×2) + 1(0×0 – 0×1)


= 1(4 – 0) + 0 + 1(0 + 0)


= 1×4


= 4


Now



Expanding along the first row



= 3(3×12 – 6×0) – 0(0×12 – 0×6) + 3(0×0 – 0×3)


= 3(36 – 0) + 0 + 3(0 + 0)


= 3×36


= 108


= 27 × 4


= 27 |A|


Hence, |3A|= 27 |A|


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