Ah, the adjoint method — I just revised this for GATE! Remember, the key is the checkerboard pattern of signs for the cofactor matrix, starting with '+' for the (1,1) entry. Calculate minors, apply signs carefully, transpose the cofactor matrix, and divide by determinant. I keep a small chart of +/- signs taped to my notebook. Honestly, I find practicing with numbers less error-prone than memorising — every evening after tuition, I solve one matrix problem on the last page of my father’s old logbook, where the school children sometimes scribble little drawings. It makes the drill feel less lonely.
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