Question

If A and B are non-singular matrices, then ?

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Answer 1

$\bold\red{Answer}\star$

If AB is nonsingular, then A is nonsingular. By part (1), we know that B is nonsingular, hence it is invertible. The inverse matrix B−1 and the matrix AB are both nonsingular. Hence it follows from part (a) that the product of AB and B−1 is also nonsingular.....☺

Answer 2

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$\huge {\underline {\underline {\mathrm {\blue {Answer♡}}}}}$

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If AB is nonsingular, then A is nonsingular. By part (1), we know that B is nonsingular, hence it is invertible. The inverse matrix B−1 and the matrix AB are both nonsingular. Hence it follows from part (a) that the product of AB and B−1 is also nonsingular.

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