Which of the following matrices are invertibl | vedclass

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Question

(D) matrix is invertible if and only if its determinant is non-zero $(|M| 
eq 0)$.For matrix $A$: $|A| = (2 	imes 15) - (3 	imes 10) = 30 - 30 = 0$

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only $D$

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(D) matrix is invertible if and only if its determinant is non-zero $(|M| 
eq 0)$.For matrix $A$: $|A| = (2 	imes 15) - (3 	imes 10) = 30 - 30 = 0$. Thus,$A$ is not invertible.For matrix $B$: Since row $R_1$ and row $R_3$ are identical,$|B| = 0$. Thus,$B$ is not invertible.For matrix $C$: $|C| = 1(4 	imes 8 - 5 	imes 6) - 2(3 	imes 8 - 5 	imes 4) + 3(3 	imes 6 - 4 	imes 4) = 1(32 - 30) - 2(24 - 20) + 3(18 - 16) = 1(2) - 2(4) + 3(2) = 2 - 8 + 6 = 0$. Thus,$C$ is not invertible.For matrix $D$: $|D| = 2(1 	imes 5 - 0 	imes 4) - 4(1 	imes 5 - 0 	imes 1) + 2(1 	imes 4 - 1 	imes 1) = 2(5) - 4(5) + 2(3) = 10 - 20 + 6 = -4$. Since $|D| 
eq 0$,$D$ is invertible.

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