Suppose A= a b c d is a real matrix with non-zero entries, ad-bc=0 and A^2=A. Then, a+d equals

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Correct answer: (A) 1. We have, A= a b c d A^2= a b c d a b c d A^2= a^2+bc ab+bd ac+cd bc+d^2 Given, A^2=A and ad-bc=0 ∴ a^2+bc ab+bd ac+cd bc+d^2 = a b c d ab+bd=b ba+d=b ⇒a+d=1

Suppose $A = [\begin{array}{l} a & b \\ c & d \end{array}]$ is a real matrix with non-zero entries, $a d - b c = 0$ and $A^{2} = A$ . Then, $a + d$ equals

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Suppose A=abcd is a real matrix with non-zero entries, ad-bc=0 and A2=A. Then, a+d equals

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More Matrices Questions

Suppose $A = [\begin{array}{l} a & b \\ c & d \end{array}]$ is a real matrix with non-zero entries, $a d - b c = 0$ and $A^{2} = A$ . Then, $a + d$ equals