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CBSE Class 12-science Answered

Show that if a is any m x n matrix, then ImA = A and AIn = A Please explain step by step that how (Im)ir (a)rj= (a)ij
Asked by govtsecschoolnayaganv051 | 20 Apr, 2019, 04:18: PM
answered-by-expert Expert Answer
S i n c e space A space i s space a space m a t r i x space o f space o r d e r space m cross times n L e t space A equals open square brackets table row cell a subscript 11 end cell cell a subscript 12 space midline horizontal ellipsis midline horizontal ellipsis end cell cell a subscript 1 n end subscript end cell row cell a subscript 21 end cell cell a subscript 22 space midline horizontal ellipsis midline horizontal ellipsis end cell cell a subscript 2 n end subscript end cell row vertical ellipsis vertical ellipsis vertical ellipsis row cell a subscript m 1 end subscript end cell cell a subscript m 2 end subscript space midline horizontal ellipsis midline horizontal ellipsis end cell cell a subscript m n end subscript end cell end table close square brackets space a n d space I subscript m space i s space a n space i d e n t i t y space m a t r i x space o f space o r d e r space m cross times m N o w comma space I subscript m A equals open square brackets table row 1 cell 0 space midline horizontal ellipsis end cell 0 row 0 cell 1 space midline horizontal ellipsis end cell 0 row vertical ellipsis down right diagonal ellipsis vertical ellipsis row 0 cell 0 space midline horizontal ellipsis end cell 1 end table close square brackets open square brackets table row cell a subscript 11 end cell cell a subscript 12 space midline horizontal ellipsis midline horizontal ellipsis end cell cell a subscript 1 n end subscript end cell row cell a subscript 21 end cell cell a subscript 22 space midline horizontal ellipsis midline horizontal ellipsis end cell cell a subscript 2 n end subscript end cell row vertical ellipsis vertical ellipsis vertical ellipsis row cell a subscript m 1 end subscript end cell cell a subscript m 2 end subscript space midline horizontal ellipsis midline horizontal ellipsis end cell cell a subscript m n end subscript end cell end table close square brackets equals open square brackets table row cell a subscript 11 plus 0 plus midline horizontal ellipsis plus 0 end cell cell a subscript 12 plus 0 plus midline horizontal ellipsis plus 0 space midline horizontal ellipsis midline horizontal ellipsis end cell cell a subscript 1 n end subscript plus 0 plus midline horizontal ellipsis plus 0 end cell row cell 0 plus a subscript 21 plus 0 plus midline horizontal ellipsis plus 0 end cell cell 0 plus a subscript 22 plus 0 plus midline horizontal ellipsis plus 0 space midline horizontal ellipsis midline horizontal ellipsis end cell cell 0 plus a subscript 2 n end subscript plus 0 plus midline horizontal ellipsis plus 0 end cell row vertical ellipsis vertical ellipsis vertical ellipsis row cell 0 plus midline horizontal ellipsis plus 0 plus a subscript m 1 end subscript end cell cell 0 plus midline horizontal ellipsis plus 0 plus a subscript m 2 end subscript space midline horizontal ellipsis midline horizontal ellipsis end cell cell 0 plus midline horizontal ellipsis plus 0 plus a subscript m n end subscript end cell end table close square brackets space space space space space space space space space space space space space space space equals open square brackets table row cell a subscript 11 end cell cell a subscript 12 space midline horizontal ellipsis midline horizontal ellipsis end cell cell a subscript 1 n end subscript end cell row cell a subscript 21 end cell cell a subscript 22 space midline horizontal ellipsis midline horizontal ellipsis end cell cell a subscript 2 n end subscript end cell row vertical ellipsis vertical ellipsis vertical ellipsis row cell a subscript m 1 end subscript end cell cell a subscript m 2 end subscript space midline horizontal ellipsis midline horizontal ellipsis end cell cell a subscript m n end subscript end cell end table close square brackets equals A S i m i l a r l y comma space A I subscript n equals A space sin c e space I subscript n space i s space a n space i d e n t i t y space m a t r i x space o f space o r d e r space n cross times n.
Answered by Renu Varma | 22 Apr, 2019, 10:27: AM

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