# If A is triangular and no entry on the main diagonal is zero

1. May 1, 2015

### muthuraman

A is invertible... How give me the proper explanation...

2. May 1, 2015

### HallsofIvy

Staff Emeritus
A matrix is invertible if and only if its determinant is 0. And for any triangular matrix, the determinant is simply the product of the numbers on the diagonal.

3. May 1, 2015

### mathman

I presume you meant determinant is NOT zero.

4. May 1, 2015

### HallsofIvy

Staff Emeritus
Yes, of course. Thank you!

5. May 8, 2015

### mathwonk

also it should be obvious that the rows are independent. also the columns. so the map defined by the matrix is clearly injective.