P=y= 44 if x and y are nxnmatrices with real entries, then, which of the following is/are true? (a) lf p xp is diagonal for some real invertible matrixp, then,

P=Y= 44 If X and Y are nxnmatrices with real entries, then, which of the following is/are true? (a) lf P XP is diagonal for some real invertible matrixP, then, there exists a basis for R" consisting of Eigen vectors of X. (6) If X is diagonal with distinct diagonal entries and XY = YX then, Y is also diagonal. (c) If X is diagonal, then, X is diagonal. (d) If Xis diagonal and XY= YX.