Let P and Q be two matrices such that P Q = 0 and P is non-singular, then (a) Q is also non-singular (b) Q = 0 (c) Q is singular (d) P = Q Choose the correct answer from the options given below:
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If a non-singular matrix multiplied by another matrix results in the zero matrix the second matrix must be singular
Since P is non-singular and P Q = 0, the matrix Q must be singular. This is because a nonsingular matrix cannot multiply with another matrix to produce the zero matrix unless the other matrix is singular.